How Are We Apart? Continuity and Change in the Structure of Ideological Disagreement in the American Public, 1980–2012

How Are We Apart? Continuity and Change in the Structure of Ideological Disagreement in the... Abstract Even after two decades of intense research, social scientists are still in disagreement over whether the American public is polarized. Starting from the premise that disagreement is multifaceted, this paper attempts to clarify how and which aspects of ideological disagreement have changed over the past few decades. Three major structural features of ideological disagreement that have been discussed under the umbrella term “polarization” are identified from the literature—polarization, partisan sorting, and dimensional alignment—and redefined into analytically distinct and non-overlapping concepts. Two different scaling methods are applied to the American National Election Studies from 1980 to 2012 in order to examine changes in how citizens organize their attitudes regarding concrete political and social issues (operational ideology) and their self-identifications with the ideological labels “liberal” and “conservative” (symbolic ideology). Results show at best mixed evidence of growing polarization. Partisan sorting has increased over time on both symbolic and operational ideology. However, it is mainly the symbolic side on which disagreement across partisan lines is most pronounced. Finally, contrary to the popular notion of a culture war dividing the United States, the public has become less polarized on moral issues, and the moral dimension of citizens’ operational ideology has become dealigned from the economic and civil rights dimension over the past decade. Introduction Two decades have passed since DiMaggio, Evans, and Bryson (1996) drew the attention of social scientists to the phenomenon of mass polarization. Their paper marked the beginning of a heated scholarly debate over whether the American public is polarized that involved not only political sociologists but also political scientists, economists, and social psychologists. However, even after twenty years of intense interdisciplinary research on the topic, there remains widespread disagreement about the phenomenon. While most social scientists agree that polarization in the US Congress has grown over the past fifty years (Bonica 2014; McCarty, Poole, and Rosenthal 2006; Poole and Rosenthal 2007), views regarding the general public differ greatly. One camp argues that citizens have become more polarized in recent decades (Abramowitz and Saunders 2008; Campbell 2016; Jacoby 2014; Layman, Carsey, and Horowitz 2006), while other scholars claim that the public has remained relatively stable in their issue preferences (Ansolabehere, Rodden, and Snyder 2006; Fiorina, Abrams, and Pope 2011; Levendusky 2009a), or even shows more consensus on several issues (Evans 2003; Fischer and Hout 2006). One reason for the conflicting views is that ideological disagreement can be structured in a variety of ways. And, depending on which of these configurations is perceived as the distinguishing feature of political disagreement, different conclusions might be reached regarding the state of public opinion. To complicate matters further, numerous studies on political polarization tend to conflate different forms of disagreement with one another, both conceptually and empirically. Hence, the precise implications of existing empirical findings remain often ambiguous. This paper attempts to clarify how and what aspects of ideological disagreement have changed since the 1980s. For this purpose, three major structural features of ideological disagreement that have been discussed under the umbrella term “polarization” are identified from the literature—polarization, partisan sorting, and dimensional alignment—and redefined into analytically distinct and mutually exclusive concepts. Admittedly, the three features do not exhaust all possibilities of how ideological disagreement might be structured. Nevertheless, they have not been integrated and compared in a longitudinal study in any of the recent contributions. While DiMaggio, Evans, and Bryson (1996) laid the groundwork for subsequent research, few have taken up their multidimensional conceptualization of political disagreement. In particular, most previous studies have focused exclusively on polarization and partisan sorting, leaving the dimensional alignment aspect relatively understudied (for a review, see Fiorina and Abrams [2008]; Fischer and Mattson [2009]; Hetherington [2009]; Layman, Carsey, and Horowitz [2006]). Yet, it is not only the disagreement on each ideological dimension per se but also how well these dimensions are aligned with one another that determines the disagreement within society as a whole. While disagreement that is tightly aligned across different ideological dimensions has the tendency to amplify political hostility, cross-cutting lines of disagreement are likely to buffer, rather than reinforce, the tension of each dimension by scattering the foci of conflict (Blau and Schwartz 1984; Coser 1956; Schattschneider 1960). Thus, any approach to the study of political disagreement that considers each ideological dimension in isolation remains necessarily incomplete. Furthermore, it is particularly the alignment of issue preferences that has undergone unexpected changes over the past decade. In this paper, I document how the three features of ideological disagreement have changed from the 1980s onward. I apply two different scaling methods to the American National Election Studies to estimate the operational and symbolic ideology of the public, where the former pertains to how citizens organize their preferences on concrete political or social issues and the latter to how they self-identify with the labels “liberal” and “conservative” (Ellis and Stimson 2012). Based on these estimates, changes in ideological disagreement are traced from 1980 to 2012. The results of the analysis show that ideological disagreement is surprisingly limited on the operational side of ideology: the ideological distributions remain largely unimodal on all dimensions, and even the divide between Democrats and Republicans is rather modest in most of the analyzed years. It is mainly the symbolic side on which partisans tend to disagree with each other. Also, I find that the moral dimension of operational ideology has depolarized and become dealigned from the economic and civil rights dimension over the past decade. Hence, the moral dimension is “cross-cutting,” rather than reinforcing, the political conflict on the traditional ideological cleavages today, thereby preventing a clear-cut bifurcation of the ideological space into two coherently opposing camps. The paper unfolds as follows. The next section defines the three disagreement concepts that will be used throughout the paper. The subsequent section presents the data and the statistical models through which the ideological disagreement of the American public will be studied. After presenting the empirical results, the paper concludes by discussing the implications of the findings. Three Ways to Disagree There is at best a weak consensus regarding the concept of polarization and how it should be measured (Hetherington 2009). While some scholars define polarization as the growing difference in political views of Democrats and Republicans (Abramowitz and Saunders 2008), others emphasize that the major characteristic of a polarized public is the bimodality of the ideological distribution (Fiorina and Abrams 2008). Still others conceptualize polarization as a property of the interrelationship between issue dimensions rather than single issues (Baldassarri and Gelman 2008; DiMaggio, Evans, Bryson 1996). Given these complexities, I start by defining three analytically distinct and mutually exclusive concepts—polarization, sorting, and dimensional alignment—which will be used to analyze how ideological disagreement is structured in the United States. Polarization and Sorting When considering a unidimensional ideological space at a specific point in time, I refer to polarization as the degree to which the ideology of the public is clustered around two separate ideological centers and how dispersed the distribution is. What is important for polarization is how far apart citizens’ positions are from one another and whether these positions are concentrated around different points. Thus, polarization is regarded as a characteristic of the shape of the overall ideological distribution. Further, polarization entails two different components that might vary independently from each other: bimodality and dispersion (DiMaggio, Evans, and Bryson 1996). The distribution of an ideological dimension might have a high variance while the shape of the distribution remains unimodal; on the other hand, the distribution can have two well-separated modes (peaks) that lie close to each other. Of course, polarization is not a binary state: a public might be more or less polarized. However, it is mainly when bimodality is combined with a high variance that we might speak of a polarized public with confidence (Fiorina and Abrams 2008). In contrast to polarization, partisan sorting is defined as the degree to which the ideology of Democrats and Republicans do not overlap with each other. It is thus a concept that captures the bivariate relationship between opinion and group membership. When all Democrats are to the left (or the right) of all Republicans, sorting is complete. If some Democrats are more conservative (or liberal) than some Republicans, sorting becomes a matter of degree. To the extent that partisanship forms a social identity (Campbell et al. 1960; Green et al. 2004), partisan sorting will mobilize more intense emotions into the political sphere as political disagreement becomes not simply about what is right or wrong but about whether “we, as a team,” are right or wrong. The consolidation of ideology and partisan identities, thus, tends to increase out-group biases and antagonism between partisan camps (Blau and Schwartz 1984; Mason 2016). Indeed, recent research has shown that hostility across partisan lines has increased over the past decades (Iyengar and Westwood 2014; Iyengar, Sood, and Lelkes 2012), and that better-sorted partisans hold more antagonistic views toward the opposing camp (Mason 2015). Polarization and sorting, as defined above, are analytically distinct concepts. Contrary to arguments that it is “logically impossible” for a perfectly sorted citizenry “not to be highly polarized” (Campbell 2016, 122), partisan sorting has, a priori, no logical implications for polarization as long as the ideological distribution of the public has at least some variability. The hypothetical distributions in figure 1 illustrate the point. The shaded area in light gray represents the overall (or marginal) ideological distribution, and the dashed black and gray lines, respectively, show the distributions of Democrats and Republicans. As we move from panel I of the figure to panel II, all Republicans change their place with Democrats who were placed to their right, so that the two groups are perfectly sorted in the latter situation. However, as the overall distribution remains unchanged, we have no increase in polarization. On the other hand, the overall distribution becomes polarized—that is, the bimodality and variance increases—as we move from panel I to panel III; yet, since the ideology of the Democrats and Republicans overlap perfectly in both cases, there is no sorting at all. This hypothetical example makes clear that an increase in sorting does not imply that polarization increases as well, and that polarization might occur without sorting. Further, it shows that conventional measurements of polarization, such as the mean difference between Democrats and Republicans, obscures the distinction between polarization and sorting: an increased mean difference between the parties may be due to sorting (a movement from panel I to II) or sorting and polarization (panel I to IV). Indeed, the difference in mean opinion might even decrease while the overall distribution becomes more polarized (panel II to III). Although the last pattern is unlikely to be observed in reality, it demonstrates how the mean differences of partisan camps can give a misleading picture of the state of disagreement. Figure 1. View largeDownload slide Four hypothetical distributions that demonstrate the difference between polarization and sorting Note: The shaded area in light gray represents the (marginal) ideological distribution of the population. Black and dark gray dashed lines and ticks represent the distribution of two subgroups of the population. Figure 1. View largeDownload slide Four hypothetical distributions that demonstrate the difference between polarization and sorting Note: The shaded area in light gray represents the (marginal) ideological distribution of the population. Black and dark gray dashed lines and ticks represent the distribution of two subgroups of the population. The definition of polarization presented here is the same as what DiMaggio, Evans, and Bryson (1996) referred to as a form of “within-population polarization” and Fiorina and Abrams (2008) as simply “polarization.” The definition of partisan sorting, on the other hand, diverges slightly from the previous literature. Increased sorting has been defined as the increase in the “correlation between” or “alignment of” partisanship and ideology, where alignment means that citizens take the same side on political issues as their parties in Congress (Levendusky 2009a, 3, 44). The definition proposed in this paper—as the lack of overlap—seems to be similar, but can lead to different conclusions in certain circumstances. For example, if sorting is defined with reference to elites, a problem arises when partisans in the public become better separated from each other, while moving in different directions than their counterparts in Congress (see, for example, Baldassarri and Park 2016; Fiorina and Levendusky 2006); on the other hand, if sorting is defined as the correlation of partisanship and ideology in the mass public, it depends partly on how extreme the ideology of the partisan groups are and, thus, conflates an aspect of polarization with sorting.1 When sorting is defined as the lack of overlap, both ambiguities are overcome: it is independent of the extremity and bimodality in ideology, and thus of what we have called polarization, and does not depend on the behavior of elites. Dimensional Alignment So far, we have implicitly assumed that the ideological space is unidimensional. However, early accounts of ideology in the United States as well as more recent research suggest that the belief system of the American public consists of at least two dimensions (Baldassarri and Goldberg 2014; Carmines, Ensley, and Wagner 2012; Layman and Carsey 2002; Lipset 1960; Treier and Hillygus 2009). The main reason for examining a multidimensional opinion space is not only because it is realistic; more importantly, it brings to the fore a new configurational aspect of disagreement that is absent in the unidimensional case—namely, the interrelationship between the dimensions on which ideology is formed. A precondition for a society to polarize into two ideologically coherent and opposing camps is that the dimensions on which ideology is formed are aligned with one another (Coser 1956; Schattschneider 1960). In the absence of alignment, the disagreement in society will remain unorganized in the sense that groups that disagree on one dimension would be equally likely to agree or disagree on other dimensions. In this case, disagreement across dimensions are “cross-cutting” one another, which prevents the concentration of “foci” (Feld 1981) of dissent. It is only when the dimensions are highly aligned that a single dimension emerges that summarizes all the disagreement in society and that two consistently opposing subgroups can form (Baldassarri and Gelman 2008). Thus, the alignment of dimensions is an indispensable element in describing how political disagreement is structured in society. Despite its importance, however, it has remained relatively understudied compared to polarization and partisan sorting, which led to the neglect of significant changes in ideological disagreement. Empirically, the concept of dimensional alignment is captured by the correlation between ideological dimensions. On the micro level, a high correlation implies that the political views of individuals show high constraint (Converse 1964); the macro-level analogue is a low level of “cross-cuttingness” between the dimensions (Lipset 1960). Note, however, that dimensional alignment is not a form of disagreement per se. Even if the ideological dimensions are highly correlated—and reduced to a single dimension—the distribution on that continuum might be centered around a single point with low variance instead of being bimodal with high variance. Rather, the correlation shapes the coherence of the belief system and, thereby, how polarization (or the lack of it) on each ideological dimension is combined to form the overall structure of polarization in society. To illustrate the point, imagine a society in which ideology has two dimensions, an economic and a social one. If the distribution on the economic dimension has a bimodal shape and the social dimension is unimodal, the joint distribution will be in general bimodal. However, with low-dimensional alignment, the subgroups thus formed will not be in consistent opposition. That is, approximately half of the members of the economically “conservative” camp will be socially “liberal,” and the same is true for the economically liberal group. Hence, in the absence of dimensional alignment, there will be an ideological dimension on which the otherwise polarized subgroups can find common ground. Furthermore, the consensus on the social dimension will “cut through” the dissent on the economic dimension and might buffer otherwise intense conflict. The way in which dimensional alignment shapes the structure of polarization in a multidimensional belief space is starkly demonstrated in the case where the ideological distribution on all dimensions is bimodal. Figure 2 shows 5,000 simulated samples from two bimodal distributions with correlation set to ρ = 0,0.3,0.6,0.9. Note that for each graph, the marginal distributions—shown as histograms at the margins of each plot—are polarized and look approximately the same. It is only the correlation between the dimensions that changes. Panel (a) of figure 2 shows the joint distribution where economic and social dimensions are uncorrelated. Although the citizens are polarized on each dimension, the disagreement of each is cross-cutting the other, so that four subgroups emerge instead of two. Also, approximately half of the hypothetical society is holding “inconsistent” opinions by being liberal on one dimension and conservative on the other. With an increase in the correlation between the dimensions, however, the number of inconsistent citizens is reduced as they are absorbed into the ideologically coherent camps. Finally, with a correlation of ρ = 0.9, we see that two large subgroups with coherently opposing views emerge, and that the ideological space can be summarized on the 45-degree line. Figure 2. View largeDownload slide Correlations and cross-cuttingness: four hypothetical distributions Note: The histograms at the margin of each panel show the marginal distributions of the two dimensions. Random draws are generated by sampling from correlated two-component normal mixture distributions using an iterative, trial-and-error algorithm proposed by Ruscio and Kaczetow (2008). Figure 2. View largeDownload slide Correlations and cross-cuttingness: four hypothetical distributions Note: The histograms at the margin of each panel show the marginal distributions of the two dimensions. Random draws are generated by sampling from correlated two-component normal mixture distributions using an iterative, trial-and-error algorithm proposed by Ruscio and Kaczetow (2008). What this simulation demonstrates is the following: only with high-dimensional alignment will polarization on each dimension lead to a polarized society. Indeed, even if ideology is highly polarized on all dimensions, 2D subgroups will form out of a D-dimensional belief space as long as the inter-dimension correlation remains sufficiently low. Society would be “fragmented” rather than polarized with low-dimensional alignment: clusters of citizens occupying distinct positions in the ideological space would emerge, but they would be in agreement on several ideological dimensions, rather than coherently contradicting one another. Therefore, although dimensional alignment is not a form of polarization per se, it determines the shape of the overall (or joint) ideological distribution in society, enabling or preventing the bifurcation of the public into two camps with consistently opposing views. Operational versus Symbolic Ideology While the term “ideology” has been defined in numerous ways (Gerring 1997; Jost, Federico, and Napier 2009), in this paper I focus on two different meanings that have been attached to the concept by scholars and pundits: namely, how citizens identify themselves with the labels “liberal” and “conservative,” and how they organize their beliefs regarding concrete political issues. Following Ellis and Stimson (2012), I refer to the former aspect as symbolic ideology and to the latter as operational ideology. It has long been thought that self-identification with liberal or conservative labels is only moderately related to concrete policy preferences (Conover and Feldman 1981; Free and Cantril 1967; Miller 1992). Indeed, in the aggregate, operational and symbolic ideology seem to contradict each other: if American citizens are asked about their self-identification, the majority identify with the conservative label; on the other hand, when asked about specific issues and policies, they tend to be “liberal” in the sense that they want more public spending, a bigger government, and more equal treatment of minorities (Stimson 2004). More important than the aggregate trends per se is that many citizens base their ideological self-identification and their issue preferences on systematically different foundations (Popp and Rudolph 2011). Some citizens associate the terms “liberal” and “conservative” with their preferences regarding the size of government; for others, however, the reason for identifying with these labels stems from their non-political connotations (Conover and Feldman 1981; Ellis and Stimson 2012).2 The distinct foundations of symbolic and operational ideology suggest that disagreement on these two “faces” of ideology might be structured in a different way. However, there has been little effort to systematically compare changes in ideological disagreement across these two sides of ideology. Most polarization scholars focus exclusively on only one of the two aspects or draw no clear distinction between symbolic and operational ideology. In some instances, measures of operational and symbolic ideology are even combined into unidimensional composite scales (e.g., Abramowitz 2010; Levendusky 2009b). Not only does this practice blur the distinction between symbolic and operational ideology but, given that operational ideology is multidimensional, it is not clear to which operational dimension the self-identification aspect belongs (Carmines, Ensley, and Wagner 2012). Therefore, in what follows, I treat the two faces of ideology separately. Data and Methods The data that are analyzed in this paper come from the American National Election Studies Time Series (ANES). Any study that tries to make comparisons across subgroups or over time with survey respondents has to address the problem of comparability. This problem is especially acute in the case of estimating latent traits, such as ideology. Since a latent variable has no natural scale, it is standard practice to normalize it to have mean zero and variance one. However, this renders the recovered latent dimension incomparable across time, unless all periods under study are scaled jointly.3 For this reason, I introduce two different scaling methods—one for operational and the other for symbolic ideology—that place all estimated ideological positions on a common scale and, thus, makes them comparable across different years. Estimation of Operational Ideology For the analysis of operational ideology, I use all political attitude measures in the ANES that meet two criteria. First, to prevent cherry-picking items that might bias the results of the analysis, I use all issues in the ANES that were administrated at least three times between 1986 and 2012. The restriction on the period is necessary because most of the moral issues that sparked the debate over the “culture war” (Fiorina, Abrams, and Pope 2011; Hunter and Wolfe 2006) are not measured before 1986. Second, I include only attitude measures that pertain to economic, civil rights, and moral issues. The items are classified following the typology in Baldassarri and Goldberg (2014). However, in this paper I do not analyze issues that belong to their foreign policy/security category, as these issues have shown rather idiosyncratic patterns in previous studies (Baldassarri and Gelman 2008; Hurwitz and Peffley 1987). The selection process leaves me with 43 items. I include all respondents that answered at least one of the attitude questions in the analysis. The list of items analyzed, their classification, and the sample sizes for each year are shown in the  appendix. To estimate the operational ideology of the respondents, I use a graded response model (GRM) (Samejima 1969). As in factor analysis, the GRM uses observed responses on a set of items to recover positions in a latent space (i.e., “factor scores”). Differently from the linear factor model, however, the GRM assumes that each item is measured on a binary or ordinal scale and uses logistic link functions to relate the latent dimensions to the responses. Thus, the GRM overcomes the unrealistic assumption of the usual factor model that the association of the latent trait and the observed responses is linear and that all observed variables are measured on a continuous scale. I use a Bayesian approach to estimate the model out of practical rather than philosophical reasons. Most importantly, by estimating the model using MCMC techniques, natural uncertainty estimates of the latent positions (and any function thereof) are easily obtained, which is not the case when the model is fit by maximum likelihood. I use weakly informative priors for all parameters in the model. To identify the latent scale, I fix the prior mean of each latent dimension in the first year of the analysis to zero and fix one discrimination parameter for each latent dimension equal to one.4 Also, as in confirmatory factor analysis, I do not allow for cross-loadings in most of the models. All inference is drawn by sampling from the joint posterior distribution of the parameters using a Hamiltonian Monte Carlo algorithm (the No-U-Turn Sampler) implemented in STAN. For each specification of the model, I run six independent chains with 15,000 iterations. The first 10,000 iterations of each chain are discarded as “burn-in,” and inference is drawn from the remaining 5,000 iterations, which are sampled with a thinning interval of 20. The traceplots of all models that are presented below showed strong signs of convergence, with the potential scale reduction factor, Rˆ (Gelman et al. 2014, ch. 11), being estimated to be below 1.05 for all parameters in all models. Convergence statistics and posterior predictive checks for the final model, as well as details on model specification and estimation, can be found in online appendix A. Estimation of Symbolic Ideology The analysis of symbolic ideology appears to be much simpler, as the ANES includes a direct measurement of it: namely, the seven-point liberal-conservative self-placement item. A potential threat to the direct analysis of the item is that the response categories—“extremely liberal” to “extremely conservative”—might have different meanings for different respondents (Aldrich and McKelvey 1977; Levendusky 2009b), a problem known as differential item functioning (Hare et al. 2015). In their path-breaking paper, Aldrich and McKelvey (1977) proposed a method to correct differential item functioning (DIF) of the seven-point liberal-conservative item, which is similar to the “anchoring vignette” approach of King et al. (2004). The basic idea behind the Aldrich-McKelvey (A-M) scaling is to assume that the political stimuli—that is, politicians and political parties—have fixed position on a unidimensional latent scale, so that the positions of the respondents can be evaluated relative to these fixed points. For example, if respondent i states that she is “moderate” but places Barack Obama and Mitt Romney, respectively, in the “slightly conservative” and “extremely conservative” category, she would be estimated to be more liberal than respondent j, who says that he is “extremely liberal” but places Obama into the same “extremely liberal” category and Mitt Romney into the “liberal” category. Since respondents are asked in each year of the ANES to place not only themselves but also several political stimuli on the same seven-point liberal-conservative scale, it is possible to infer the position of each respondent relative to the fixed stimuli positions. Further, as these “corrected” positions of the respondents are all evaluated relative to the same set of stimuli, they lie on a common scale and are therefore comparable. In a recent analysis, Hare et al. (2015) applied a Bayesian version of A-M scaling to the ANES, and found that the electorate is more polarized than the (unscaled) raw responses suggest. The analysis was, however, restricted to a single year, namely 2012. One of the reasons for the restriction lies in the limitation of the method in estimating a common scale on which all corrected positions can be placed over time. To overcome this “bridging” problem, I project the responses on the seven-point liberal-conservative item into a scale that satisfies two conditions: (1) it approximately measures the same liberal-conservative dimension on which the respondents are asked to place the stimuli (and themselves); and (2) it remains constant over the entire period of the study. An obvious candidate for such a scale is the first dimension of the Common Space DW-NOMINATE scores (Poole and Rosenthal 2007). The DW-NOMINATE scores measure the ideology of legislators by scaling their roll-call voting patterns and are widely regarded as the standard ideological measure of members of Congress. The first dimension of the DW-NOMINATE scores is typically interpreted as the liberal-conservative dimension, while the second dimension measures a racial/regional dimension. Importantly, the explanatory power of the second dimension has rapidly declined in the late 1970s, so that, from the 1980s onward, ideology in Congress is regarded as unidimensional and only the first dimension is used (Poole and Rosenthal 2007). Also, as the NOMINATE scores are estimated on the same scale across different years, they satisfy the two conditions outlined above. The projection is done as follows. First, I select all political figures who 1) served either in Congress or as president; and 2) were placed by the respondents on the seven-point liberal-conservative scale between 1980 and 2012 in the ANES. Thereafter, I regress the (first dimension) DW-NOMINATE scores of these figures, plus the median score of each party in each year, on the respondents’ placements of these stimuli. As the estimated regression coefficients reflect how respondents distort the positions of the stimuli, the linear projection of the self-placements into the NOMINATE space “corrects” for the DIF in the same way as the A-M scaling procedure. Indeed, in online appendix A, it is shown that the projection method is mathematically equivalent to A-M scaling, except that the NOMINATE scores are used to estimate the stimuli positions, whereas the original model estimates these positions from survey responses. The crucial assumption underlying this method is that the seven-point liberal-conservative item of the ANES measures approximately the same dimension as the NOMINATE scores. Fortunately, this assumption can be tested, at least indirectly. Since A-M scaling has been shown to perform well on public opinion data (Armstrong et al. 2014; Palfrey and Poole 1987), I correlate the corrected measures obtained by A-M scaling with those obtained from the projection method within each year. Also, I estimate the same projection model using CF scores, which estimate politicians’ ideology from over 100 million records of campaign finance data (Bonica 2014), in place of the NOMINATE scores as a second robustness check. A high correlation coefficient between these estimates indicates that the sets of corrected positions measure approximately the same scale up to an affine transformation. In the analysis of the symbolic ideology, I use the presidential election years from 1980 to 2012. I restrict the analysis to this period because of the following reasons. First, it is only after the late 1970s that the ideological space measured by the NOMINATE scores has become unidimensional (Poole and Rosenthal 2007). Thus, the projection method has face validity only for the post-1980 period. The restriction to the presidential election years is necessary because only one political figure (the incumbent president) is placed on the seven-point liberal-conservative scale by all respondents in congressional election years. Respondents who placed fewer than three stimuli on the seven-point liberal-conservative item or failed to place themselves on the scale were not included in the analysis. The Common Space DW-NOMINATE scores and the CF scores for available political figures over the period 1980–2012 are shown in table 1. Table 1. Common Space DW-NOMINATE Scores and CF Scores of Political Stimuli in the ANES Stimuli  NOMINATE  CF scores  Stimuli  NOMINATE  CF scores  Anderson  0.187  −0.663  Gore  −0.336  −0.894  Brown  —  −0.651  Jackson  —  −0.761  Buchanan  —  1.258  T. Kennedy  −0.460  −0.885  H. W. Bush  0.578  0.796  Kerry  −0.373  −0.956  W. Bush  0.729  0.922  McCain  0.38  0.68  Carter  −0.521  −0.38  Mondale  −0.447  −0.798  Clinton  −0.452  −0.899  Nader  —  −1.338  Connally  —  0.893  Obama  −0.368  −1.351  Dole  0.328  0.6  Perot  —  0.447  Dukakis  —  −0.824  Reagan  0.688  0.987  Ford  0.501  —  Romney  —  0.879  Stimuli  NOMINATE  CF scores  Stimuli  NOMINATE  CF scores  Anderson  0.187  −0.663  Gore  −0.336  −0.894  Brown  —  −0.651  Jackson  —  −0.761  Buchanan  —  1.258  T. Kennedy  −0.460  −0.885  H. W. Bush  0.578  0.796  Kerry  −0.373  −0.956  W. Bush  0.729  0.922  McCain  0.38  0.68  Carter  −0.521  −0.38  Mondale  −0.447  −0.798  Clinton  −0.452  −0.899  Nader  —  −1.338  Connally  —  0.893  Obama  −0.368  −1.351  Dole  0.328  0.6  Perot  —  0.447  Dukakis  —  −0.824  Reagan  0.688  0.987  Ford  0.501  —  Romney  —  0.879  Table 1. Common Space DW-NOMINATE Scores and CF Scores of Political Stimuli in the ANES Stimuli  NOMINATE  CF scores  Stimuli  NOMINATE  CF scores  Anderson  0.187  −0.663  Gore  −0.336  −0.894  Brown  —  −0.651  Jackson  —  −0.761  Buchanan  —  1.258  T. Kennedy  −0.460  −0.885  H. W. Bush  0.578  0.796  Kerry  −0.373  −0.956  W. Bush  0.729  0.922  McCain  0.38  0.68  Carter  −0.521  −0.38  Mondale  −0.447  −0.798  Clinton  −0.452  −0.899  Nader  —  −1.338  Connally  —  0.893  Obama  −0.368  −1.351  Dole  0.328  0.6  Perot  —  0.447  Dukakis  —  −0.824  Reagan  0.688  0.987  Ford  0.501  —  Romney  —  0.879  Stimuli  NOMINATE  CF scores  Stimuli  NOMINATE  CF scores  Anderson  0.187  −0.663  Gore  −0.336  −0.894  Brown  —  −0.651  Jackson  —  −0.761  Buchanan  —  1.258  T. Kennedy  −0.460  −0.885  H. W. Bush  0.578  0.796  Kerry  −0.373  −0.956  W. Bush  0.729  0.922  McCain  0.38  0.68  Carter  −0.521  −0.38  Mondale  −0.447  −0.798  Clinton  −0.452  −0.899  Nader  —  −1.338  Connally  —  0.893  Obama  −0.368  −1.351  Dole  0.328  0.6  Perot  —  0.447  Dukakis  —  −0.824  Reagan  0.688  0.987  Ford  0.501  —  Romney  —  0.879  Measurement of Disagreement To examine how polarization, as the term was defined above, has changed over time, it is necessary to consider both the bimodality and dispersion of ideological distributions. However, there seems to be no agreed-upon measure that reliably captures the bimodality of distributions, let alone both bimodality and dispersion.5 Therefore, I rely predominantly on kernel density estimators and graphical methods in examining changes in polarization. For the changes in dispersion, however, I also analyze trends in the standard deviation of each dimension. Partisan sorting is measured by the coefficient of overlapping (Schmid and Schmidt 2006; Levendusky and Pope 2011), which is defined as   OVL(X,Y)=∫min{f(x),g(x)}dx,where f and g are, respectively, the density functions for Democrats and Republicans defined over a common ideological dimension. The coefficient of overlapping measures the density of the overlapping region between two distributions. It is equal to 1 if the densities f and g overlap perfectly and 0 if the densities are defined over disjoint domains. For less extreme cases, OVL(X,Y) lies between 0 and 1. As figure 3 illustrates, the coefficient of overlapping is an ideal measure of partisan sorting, since (one minus) the coefficient corresponds to the very definition of the concept—namely, the lack of overlap between Democrats and Republicans. The coefficient is estimated with the consistent estimator   OVL^(x1,…,xn,y1,…,ym)=1n∑i=1nI{fˆ(xi)<gˆ(xi)}(xi)+1m∑j=1mI{gˆ(yj)≤fˆ(yj)}(yj),where the xi’s and yj’s are, respectively, the sample points of Democrats and Republicans, fˆ and gˆ are kernel density estimators of f and g, and IA(u) is an indicator function that is 1 if u ∈ A and 0 otherwise. Figure 3. View largeDownload slide Hypothetical distributions of Democrats, f, and Republicans, g. The coefficient of overlapping measures the overlapping region of the two distributions. Figure 3. View largeDownload slide Hypothetical distributions of Democrats, f, and Republicans, g. The coefficient of overlapping measures the overlapping region of the two distributions. Finally, the degree of dimensional alignment is measured by the Pearson correlation coefficient between ideological dimensions. As discussed above, the inter-dimension correlation reflects the degree to which one dimension can be represented as a linear transformation of the other. Hence, the closer the correlation is to one, the higher the alignment of disagreement across the dimensions. Since the projection method results in a unidimensional continuum, the analysis of dimension alignment will be restricted to the operational aspect of ideology. Results Dimensionality of Operational Ideology While ideology in Congress has become unidimensional after the 1980s (Poole and Rosenthal 2007), how many dimensions best summarize the issue preferences of citizens remains a debated topic among social scientists (Carmines, Ensley, and Wagner 2012; Jost, Federico, Napier 2009). Hence, before we can analyze how disagreement changed over time, we need to determine the number of latent dimensions that best represents the operational ideology of the public. For this task, I fit eight different models to the data and compare their fit by the Watanabe-Akaike information criterion (WAIC). The WAIC is used to compare the out-of-sample predictive accuracy of the fitted Bayesian models, with smaller values indicating a better fit of the model (Gelman et al. 2014). The results are shown in table 2. Table 2. WAIC Values for Different Model Specifications of the Graded Response Model Model  Dim  Latent dimensions  WAIC  elpd  pˆ  Mean  Var.  Corr.  Model 8  3  Y  Y  Y  1327409.78  −663704.89  41983.90  Model 7  3  C  Y  Y  1327839.23  −663919.61  42332.66  Model 6  3  C  C  Y  1327965.44  −663982.72  42391.69  Model 5  3  C  C  C  1328053.69  −664026.84  42532.59  Model 4  2  C  C  C  1338523.14  −669261.57  32125.74  Model 3  2  C  C  C  1343005.45  −671502.72  31493.66  Model 2  2  C  C  C  1349263.22  −674631.61  29975.46  Model 1  1  C  C  —  1363502.33  −681751.16  18614.27  Model  Dim  Latent dimensions  WAIC  elpd  pˆ  Mean  Var.  Corr.  Model 8  3  Y  Y  Y  1327409.78  −663704.89  41983.90  Model 7  3  C  Y  Y  1327839.23  −663919.61  42332.66  Model 6  3  C  C  Y  1327965.44  −663982.72  42391.69  Model 5  3  C  C  C  1328053.69  −664026.84  42532.59  Model 4  2  C  C  C  1338523.14  −669261.57  32125.74  Model 3  2  C  C  C  1343005.45  −671502.72  31493.66  Model 2  2  C  C  C  1349263.22  −674631.61  29975.46  Model 1  1  C  C  —  1363502.33  −681751.16  18614.27  Note: Dim = number of latent dimensions; WAIC = Watanabe-Akaike information criterion; elpd = expected log predictive density; pˆ = effective number of parameters; C = common prior for all years; Y = year-specific prior. Table 2. WAIC Values for Different Model Specifications of the Graded Response Model Model  Dim  Latent dimensions  WAIC  elpd  pˆ  Mean  Var.  Corr.  Model 8  3  Y  Y  Y  1327409.78  −663704.89  41983.90  Model 7  3  C  Y  Y  1327839.23  −663919.61  42332.66  Model 6  3  C  C  Y  1327965.44  −663982.72  42391.69  Model 5  3  C  C  C  1328053.69  −664026.84  42532.59  Model 4  2  C  C  C  1338523.14  −669261.57  32125.74  Model 3  2  C  C  C  1343005.45  −671502.72  31493.66  Model 2  2  C  C  C  1349263.22  −674631.61  29975.46  Model 1  1  C  C  —  1363502.33  −681751.16  18614.27  Model  Dim  Latent dimensions  WAIC  elpd  pˆ  Mean  Var.  Corr.  Model 8  3  Y  Y  Y  1327409.78  −663704.89  41983.90  Model 7  3  C  Y  Y  1327839.23  −663919.61  42332.66  Model 6  3  C  C  Y  1327965.44  −663982.72  42391.69  Model 5  3  C  C  C  1328053.69  −664026.84  42532.59  Model 4  2  C  C  C  1338523.14  −669261.57  32125.74  Model 3  2  C  C  C  1343005.45  −671502.72  31493.66  Model 2  2  C  C  C  1349263.22  −674631.61  29975.46  Model 1  1  C  C  —  1363502.33  −681751.16  18614.27  Note: Dim = number of latent dimensions; WAIC = Watanabe-Akaike information criterion; elpd = expected log predictive density; pˆ = effective number of parameters; C = common prior for all years; Y = year-specific prior. Model 1 fits a unidimensional model with no distinctions between economic, civil rights, and moral issues. Model 2, model 3, and model 4 are two-dimensional models, where the economic items load exclusively on one dimension and the morality items on the other dimension. The civil rights items load only on the moral dimension in model 2, load only on the economic dimension in model 3, and are allowed to load on both the economic and moral dimension in model 4. The last four models fit three-dimensional latent structures to the data, where each dimension is estimated from items pertaining to economic, civil rights, and moral issues. Model 5 estimates a single variance-covariance matrix of the latent dimensions for all years. The rest of the models relax the assumption of model 5 by estimating separate inter-dimension correlations (model 6), correlations and standard deviations (model 7), and correlations, standard deviations, and means (model 8) for each year. Table 2 shows clearly that a three-dimensional latent structure fits the data better than single- or two-dimensional ones. Model 8 has the lowest WAIC, which suggests that it fits the data best among the proposed models. Posterior predictive checks show that model 8 reproduces the observed response patterns in the data reasonably well (see online appendix A). In line with previous studies that argued that domain-specific principles guide political attitudes (e.g., Feldman and Zaller 1992; Goren 2012) and that ideology is multidimensional (Layman and Carsey 2002; Lipset 1960; Treier and Hillygus 2009), this result renders questionable the assumption that political preferences are organized on a single dimension, as it was often assumed in the study of polarization. Thus, in the following analysis of operational ideology, the three dimensions will be treated separately. Operational Ideology: Polarization, Sorting, and Dimensional Alignment How has ideological disagreement changed over time? Figure 4 shows the density of posterior means of respondents’ ideological positions on the economic, civil rights, and moral dimension. Only three years—the first (1988), middle (2000), and last (2012) presidential election year of the data—are shown in the figure for clarity. As evident from figure 4, none of the distributions has a bimodal shape. Furthermore, while it has been argued that the ideological distribution of voters is bimodal (Abramowitz 2010), I find no indication of bimodality in any of the distributions even when the sample is restricted to individuals who reported to have voted in the last election.6 Thus, when polarization is measured in terms of bimodality, we can safely conclude that the electorate is not and has not been polarized on any of the three dimensions: most citizens hold moderate, rather than extreme, issue preferences. Figure 4. View largeDownload slide Kernel density estimates of ideological distribution: operational ideology, 1988–2012 Note: Figure shows estimated distribution of posterior means. Distributions for all analyzed years are shown in online appendix A. Figure 4. View largeDownload slide Kernel density estimates of ideological distribution: operational ideology, 1988–2012 Note: Figure shows estimated distribution of posterior means. Distributions for all analyzed years are shown in online appendix A. Figure 4 indicates also that the variance of the economic and civil rights dimension has increased, while, on the moral dimension, the dispersion first increases and then decreases again. To further explore how the dispersion has changed, I plot the estimated standard deviation of each dimension from 1986 to 2012 in the first row of figure 5.7 The figure shows that it is mainly the economic dimension on which the dispersion has continuously grown. The standard deviation of the civil rights dimension increases as well, but the trend is less consistent and might be due to the unusually high variance in the last year. Figure 5. View largeDownload slide Trends in standard deviations, coefficients of overlapping, and correlations: operational ideology, 1986–2012 Note: Standard deviations, coefficients of overlapping, and correlations are calculated based on 50 posterior draws from the joint latent ideological distribution to summarize the uncertainty in the estimates. Smoothed (LOESS) time trends for each posterior draw are shown in light gray. Figure 5. View largeDownload slide Trends in standard deviations, coefficients of overlapping, and correlations: operational ideology, 1986–2012 Note: Standard deviations, coefficients of overlapping, and correlations are calculated based on 50 posterior draws from the joint latent ideological distribution to summarize the uncertainty in the estimates. Smoothed (LOESS) time trends for each posterior draw are shown in light gray. The most surprising result is found on the moral dimension. Contradicting the widely publicized rhetoric of a “culture war” (Fiorina, Abrams, and Pope 2011; Frank 2004; Hunter and Wolfe 2006; Jacoby 2014), the moral dimension is the only domain for which we can safely conclude that no polarization has occurred no matter how it is measured. Quite to the contrary, the standard deviation of the moral domain shows an inverse U-shaped pattern over time: after a rapid increase from 1988 to the mid-1990s, it has declined sharply over the past decade. In other words, in terms of the variance of the ideological distribution, citizens were less polarized on moral issues in 2012 compared to 1998. Next, we turn to partisan sorting and dimensional alignment. The second row of figure 5 shows how the overlap between the distributions of Democrats and Republicans has changed from 1986 to 2012. Consistent with existing literature on partisan sorting, the public is better sorted on all three dimensions of operational ideology compared to thirty years ago. However, it is also apparent that the absolute degree of sorting is far from perfect. Over the entire period under analysis, the ideological distributions of Democrats and Republicans overlap more than 50 percent. Thus, even though sorting has increased, there seems to be more agreement than disagreement across partisan lines. The only exception is the economic dimension in the year 2012, where Democrats and Republicans, responding to the Great Recession, moved rapidly in opposite directions on issues such as redistribution and market regulation (Brooks and Manza 2013). As with polarization, the most intriguing finding with respect to partisan sorting pertains to the moral dimension. After showing a consistent decline up to the mid-1990s, the overlap between Democrats and Republicans has remained at the same level and even shows signs of an increase over the past decade. Note also that in none of the years are citizens better sorted on the moral dimension than on the other two dimensions. Hence, it is mainly on the economic and civil rights dimension that the views of Democrats and Republicans have constantly diverged. Changes in dimensional alignment are shown in last row of figure 5. Except for the unusually high estimates in 1986, the correlation between the economic and civil rights dimension has stayed fairly stable between 0.6 and 0.7. On the other hand, the correlation between the moral dimension and the other two dimensions shows a clear inverse U-shaped pattern. This suggests that the American public has not become more constrained in its ideology. And the moral dimension, after becoming rapidly aligned with the other two dimensions from 1986 to 1996, is cross-cutting the traditional ideological divide on economic and civil rights dimension once again. In light of the simulation shown in figure 2, this suggests that the potential of the American public to become split into two coherently opposing camps has in fact decreased over the past decade. Symbolic Ideology: Polarization and Partisan Sorting As the last step of the analysis, we turn to the symbolic aspect of ideology—that is, how respondents identify themselves with the labels “liberal” and “conservative.” Table 3 presents how the scaled positions obtained from the projection into the first dimension of the DW-NOMINATE space correlate with other measures of symbolic ideology. The within-year correlations between the projected positions and those obtained from Aldrich-McKelvey scaling are extremely high. Also, the stimuli positions recovered from the A-M procedure showed a strong linear relationship with the original DW-NOMINATE scores (r = 0.929). This result is in line with previous research, which argued that the electorate holds a quite accurate view of where politicians and parties stand once DIF is accounted for (Aldrich and McKelvey 1977; Armstrong et al. 2014; Palfrey and Poole 1987).8 Table 3. Correlations of Scaled Positions Estimated by Projection into the NOMINATE Space with 1) Raw Self-Placements on the Liberal-Conservative Seven-Point Item, 2) Estimates Obtained from Aldrich-McKelvey Scaling, and 3) Estimates Obtained from Projections into the CF Score Space Year  1980  1984  1988  1992  1996  2000  2004  2008  2012  1. Raw  0.561  0.501  0.571  0.627  0.688  0.619  0.755  0.606  0.609  2. A-M  0.978  0.990  0.978  0.995  0.999  0.993  0.997  0.999  0.999  3. CF  0.926  0.994  0.859  0.908  0.935  0.958  0.924  0.990  0.916  Obs.  960  1453  1279  1677  1289  587  875  1540  1365  Year  1980  1984  1988  1992  1996  2000  2004  2008  2012  1. Raw  0.561  0.501  0.571  0.627  0.688  0.619  0.755  0.606  0.609  2. A-M  0.978  0.990  0.978  0.995  0.999  0.993  0.997  0.999  0.999  3. CF  0.926  0.994  0.859  0.908  0.935  0.958  0.924  0.990  0.916  Obs.  960  1453  1279  1677  1289  587  875  1540  1365  Note: The last row shows the number of respondents that were used in the scaling procedure. In 2000, half of the respondents were randomly assigned to the branching version of the self-placement question. These respondents were excluded from the analysis. Table 3. Correlations of Scaled Positions Estimated by Projection into the NOMINATE Space with 1) Raw Self-Placements on the Liberal-Conservative Seven-Point Item, 2) Estimates Obtained from Aldrich-McKelvey Scaling, and 3) Estimates Obtained from Projections into the CF Score Space Year  1980  1984  1988  1992  1996  2000  2004  2008  2012  1. Raw  0.561  0.501  0.571  0.627  0.688  0.619  0.755  0.606  0.609  2. A-M  0.978  0.990  0.978  0.995  0.999  0.993  0.997  0.999  0.999  3. CF  0.926  0.994  0.859  0.908  0.935  0.958  0.924  0.990  0.916  Obs.  960  1453  1279  1677  1289  587  875  1540  1365  Year  1980  1984  1988  1992  1996  2000  2004  2008  2012  1. Raw  0.561  0.501  0.571  0.627  0.688  0.619  0.755  0.606  0.609  2. A-M  0.978  0.990  0.978  0.995  0.999  0.993  0.997  0.999  0.999  3. CF  0.926  0.994  0.859  0.908  0.935  0.958  0.924  0.990  0.916  Obs.  960  1453  1279  1677  1289  587  875  1540  1365  Note: The last row shows the number of respondents that were used in the scaling procedure. In 2000, half of the respondents were randomly assigned to the branching version of the self-placement question. These respondents were excluded from the analysis. The estimated distribution of the corrected positions is shown in the first column of figure 6.9 The solid line and dashed line represent, respectively, the estimated density based on projections into the NOMINATE and CF score space. As shown in the figure, none of the estimated distributions has a bimodal shape and much of the density is concentrated at the center in each year. On the other hand, the variance of the distributions is increasing over time. Hence, similarly to the findings on the economic dimension of operational ideology, most citizens are still holding moderate views despite an increased dispersion of the ideological distribution. Again, the same conclusion also holds when the analysis is restricted to voters.10 Figure 6. View largeDownload slide Estimated distribution of symbolic ideology (left) and coefficient of overlapping (right), 1980–2012 Note: Solid and dashed lines of the density plots, respectively, represent kernel density estimates based on projections into the NOMINATE and CFscore space. A comparison between the distributions of raw and scaled self-placements are shown in online appendix B. Figure 6. View largeDownload slide Estimated distribution of symbolic ideology (left) and coefficient of overlapping (right), 1980–2012 Note: Solid and dashed lines of the density plots, respectively, represent kernel density estimates based on projections into the NOMINATE and CFscore space. A comparison between the distributions of raw and scaled self-placements are shown in online appendix B. The right panel of figure 6 shows how the overlap in the distributions of Democrats and Republicans changed. In comparison to what was found in the case of operational ideology, where the majority of the partisans overlapped in their views, partisans are much better sorted on the symbolic side. The overlap between the distributions of Democrats and Republicans has been continuously declining for both sets of corrected ideological positions. Note that this is not true when the overlap is calculated on the raw self-placements, in which case the overlap remains fairly stable after 1996. Although the general gap in the overlap coefficients between the scaled and raw estimates seems to be due to the categorical nature of the self-identification item, the divergence between the time trends from 2004 to 2012 is clearly attributable to the correction of differential item functioning. Hence, it is true that DIF problem suppresses the amount of political disagreement. In contrast to what Hare et al. (2015) argue, however, it is not polarization but sorting that the problem is suppressing. Substantively more important is the absolute degree of sorting that is observed. The estimated overlap between Republicans and Democrats dropped from 0.45 (95 percent CI: [0.41, 0.50]) in 1980 to 0.33 (95 percent CI: [0.26, 0.33]) in 2012.11 In other words, even in 1980, partisans were more in disagreement than agreement and, by 2012, only about a third of them overlapped in their symbolic ideology.12 Hence, although sorting has increased on both operational ideology and symbolic ideology, it is mainly on the symbolic side that partisans hold well-separated views. Discussion and Conclusion Over the past two decades, the dominant question that guided research on polarization has been how much, or to what extent, the American public is polarized. Even polarization and partisan sorting have been often discussed as if they pertain to the same facet of disagreement and differ only in their intensity. This paper, on the other hand, returned to questions posed at the very beginning of the polarization debate, namely the emphasis of DiMaggio, Evans, and Bryson (1996) that polarization should be thought of as a multidimensional concept. Hence, the question asked in this paper might be summarized as “how are we apart?” instead of “how far are we apart?” The empirical analysis found two opposing currents in the time trends with regard to polarization. While none of the distributions of either operational or symbolic ideology had a bimodal shape in any year, the variance has increased for symbolic ideology as well as the economic dimension of operational ideology from the 1980s onward. The different findings with respect to extremism and bimodality offer a reason for why even scholars who make a clear distinction between polarization and sorting reach different conclusions regarding how ideological disagreement has changed over the past decades. If polarization is defined in terms of the spread of the ideological distribution, there exists some evidence for polarization; if the essential characteristic of polarization is the existence of two opposing camps—and hence bimodality—evidence for polarization is at best weak if not nonexistent. The analytical distinction between the symbolic and operational aspects of ideology is demonstrated to be fruitful in the analysis as well. While most social scientists agree that the American public is better sorted nowadays, what has gone relatively unnoticed is that the absolute degree of partisan sorting is surprisingly limited on the operational side of ideology. Indeed, partisans seem to be more in agreement than disagreement across all dimensions, except for the economic dimension in 2012. On the symbolic side of ideology, the picture looks entirely different: here, we find that partisans differed significantly in their ideology even in 1988 and, by 2012, the ideological overlap between partisan camps dropped to 30 percent. Hence, the statement that partisans differ sharply in their ideology today is only valid for symbolic ideology; for the operational side of ideology, most citizens hold similar views even if their partisanship differs. This suggests that future studies on political disagreement should make a clear distinction between the two “faces” of ideology in their analysis. Finally, throughout the analysis of operational ideology, the moral dimension showed distinct time trends on all forms of disagreement. Until the late 1990s, the moral dimension became increasingly similar to the economic and civil rights dimension. Not only did the dispersion grow, but partisan sorting evidenced a rapid surge as well. Based on these symptoms, it appeared as if morality would become another axis that reinforces the conflict on the traditional ideological cleavages (Baldassarri and Gelman 2008; Layman and Carsey 2002). In analyzing additional years of the ANES, this study showed that previous accounts are only valid for the premillennial period. With the turn of the century, all previously observed trends on the moral dimension are showing signs of a reversal: the variance dropped sharply, and partisan sorting started to show signs of a decline as well. Furthermore, the moral dimension became less correlated with—and thus dealigned from—the other two dimensions of operational ideology over the past decade, a finding that has been overlooked in previous research. These findings suggest that the reports of a “culture war” are likely exaggerated. The distribution of moral ideology is not, and has not been, bimodal at any time point, partisans were never as sharply divided in their moral ideology compared to their economic or civil rights ideology, and the variance of moral ideology is back to its level of the 1980s. Further, if the depolarization and dealigning trend continues, the moral dimension will have the potential to buffer the disagreement on the other dimensions rather than reinforcing it. This does not mean that conflict on economic or civil rights issues will be reduced due to changes in moral ideology. Instead, even if the public were to become deeply divided on economic or civil rights issues, it will not be difficult to find citizens of the opposing camps sharing similar moral views. This, in turn, will prevent the public from splitting into two consistently opposing subgroups. Of course, this conclusion depends on whether moral issues will maintain their salience in the future. If the continuation of the trends on the moral dimension—decreasing variance, sorting, and inter-dimension correlation—pushes moral issues out of the political discourse, the integrative function of cross-cutting disagreement (Baldassarri and Gelman 2008; Blau and Schwartz 1984; Coser 1956; Schattschneider 1960) will be necessarily reduced. Moral issues would come up less frequently in public as well as private conversations, so citizens might not realize that there is a set of issues on which they can agree; or even if they do, these commonalities might be taken for granted and regarded as politically irrelevant. If so, moral issues would become obsolete and “displaced” (Schattschneider 1960) by other issues. That said, a critique that moral issues were lacking in salience during the period of analysis would be mistaken. Indeed, if there was a period in which the analyzed moral issues were salient, it would be the period under study. Not only was the narrative of the culture war a product of the 1990s and the early 2000s, but it was argued that “conflict extension” (Layman and Carsey 2002; Layman, Carsey, and Horowitz 2006) rather than “conflict displacement” (Schattschneider 1960; Sundquist 1983) has been characterizing the dynamics of public opinion—that is, that the conflict on economic issues has spread over to civil rights and moral issues rather than one being replaced by others. The findings of the analysis offer an important qualification to these interpretations, at least with respect to the moral dimensions over the past decade. Of course, it might be that new moral issues will emerge in the future, become aligned with the conflict on other dimensions, and reinvigorate the culture war. Whether the moral dimension will continue to cut through the disagreement of other dimensions, reemerge as a polarizer, or lose its political importance remains to be seen. Finally, the peculiar trend on the moral dimension sheds some new lights on how public opinion is formed and changed. It is remarkable that the post-millennial reversal in moral ideology occurred in a period when ideology in Congress became unidimensional and polarized. Indeed, if citizens were cue takers, following their counterparts in Congress as it is usually assumed (Carmines and Stimson 1989; Levendusky 2009a; Zaller 1992), ideology in the public should have become a noise-added mirror image of that in Congress. Yet, while citizens followed Congress on economic and civil rights issues by sorting themselves into the “right” camps, a qualitatively different process seems to have driven moral ideology over the past decade. Utilizing a distributional, and hence aggregate, approach to political disagreement, it is difficult if not impossible to identify the micro-mechanisms responsible for the differential trajectories of the ideological dimensions. Also, in absence of an exogenous source of variation, I will have to leave it to future studies to disentangle which of the three disagreement structures was the driving force behind the reversal. We can only speculate that the aggregate trends on morality point toward a bottom-up process, with citizens leading the trend rather than being led by elites. Notes 1 A natural measure of the correlation between the ideology and partisanship would be the Pearson correlation coefficient (e.g., Baldassarri and Gelman 2008; Fiorina and Levendusky 2006) or the difference in mean ideology between Democrats and Republicans (e.g., Bafumi and Shapiro 2009; Hetherington 2009). Yet, if the most liberal Democrat and the most conservative Republican were to become more extreme over time while all others do not change their ideological position, the mean difference between the partisan groups would surely increase. Also, as long as ideology and partisanship are not already perfectly correlated, the correlation coefficient between partisanship and ideology would increase as well. This change in the ideology, however, corresponds to an increase in polarization, as the variance of the overall distribution would increase. The level of sorting, on the other hand, remains the same, since none of the Democrats has changed his or her place with any of the Republicans. 2 Clearly, symbolic ideology, as the term is defined here, does not exhaust all politically relevant symbolic identifications. For example, people might identify symbolically with social movements, their locality, or other social categories. Early studies in voting behavior (e.g., Campbell et al. 1960; Converse 1964) as well as more recent ones (Mason 2016; Perrin, Roos, and Gauchat 2014) have shown that these identifications are important in how individuals gain meaning from the political world. Further, the identification with the labels “liberal” and “conservative” is in part the result of, or at least influenced by, the identifications with such social categories. Yet, whether to include only the identification with the labels or also the identification with other social categories in the definition of symbolic ideology appears to be a definitional issue. Here, following Ellis and Stimson (2012), we take the narrow approach and confine the term to the identification with the ideological labels. 3 For example, even if the true variance of the latent dimension at time t is larger than that at time t+1, the normalizing procedure would rescale the latent dimension of each year to have the same mean and variance (namely, zero and one). 4 The discrimination parameters that I fix are as follows: I fix the government service and spending scale (VCF0839) for the economic dimension, the aid to blacks/minorities scale (VCF0830) for the civil rights dimension, and the abortion item (VCF0838) for the moral dimension. 5 For example, the kurtosis and the bimodality coefficient, which have been used in the literature, suffer from deficiencies outlined in DeCarlo (1997) and Freeman and Dale (2012). The dip test (Hartigan and Hartigan 1985), on the other hand, tests for multimodality, not bimodality. That is, a significant test statistic does not tell us whether the distribution has two, three, or more modes. More importantly, while quantifying the degree of polarization has its merits, to determine whether there is substantively meaningful polarization, graphical explorations of the whole ideological distribution offers more information than single quantitative measures. 6 All results that are referred to but not presented in the paper are included in online appendix B. 7 While it is tempting to compare the standard deviations across dimensions, this is not possible since the scale of each dimension differs. Hence, only the time trend will be interpreted. 8 Due to the failure of respondents to place the stimuli or themselves on the liberal-conservative scale, the number of observations per year are smaller than those used in the analysis of operational ideology. To the extent that the missing pattern in the data affects the results of the analysis, the bias is likely to be toward more polarization and sorting. This is because respondents who fail to place themselves and other stimuli on the liberal-conservative continuum are in general less informed, and tend to report relatively centrist positions (Zaller 1992). 9 For the sake of clarity, outlying observations are not shown. The substantive conclusion does not change when these observations are included (results presented in online appendix B). 10 Time trends of the dispersion as well as the results for the voting population can be found in online appendix B. 11 Confidence intervals were calculated using bootstrapping with 200 replications. 12 Estimating the overlap on operational ideology with only those respondents who were used in the analysis of symbolic ideology does not change the conclusion that the majority of Democrats and Republicans overlap in their operational ideology (see online appendix B). Appendix Item Classification and Parameter Estimates of Graded Response Model Table A1. Posterior Means of Discrimination ( γk) and Cut Point ( κk,c) Parameters, Graded Response Model Results Dimension  Variable  Disc.Param.  Cut 1  Cut 2  Cut 3  Cut 4  Cut 5  Cut 6  Economic  Federal spending - The homeless  1.346  1.252  3.981  —  —  —  —  Economic  Federal spending - Poor/poor people  1.278  0.354  3.581  —  —  —  —  Economic  Federal spending - Assistance to Blacks  1.191  −1.528  1.939  —  —  —  —  Economic  Less government better OR government do more  1.167  0.707  —  —  —  —  —  Economic  Federal spending - Child care  1.077  0.468  3.224  —  —  —  —  Economic  Federal spending - Welfare programs  1.004  −1.843  0.628  —  —  —  —  Economic  Government services/spending scale  1.000  −2.688  −1.588  −0.371  1.280  2.475  3.724  Economic  Federal spending - food stamps  0.970  −1.857  1.095  —  —  —  —  Economic  Govt too involved in things OR problems require  0.928  0.506  —  —  —  —  —  Economic  Guaranteed jobs and income scale  0.879  −2.486  −1.692  −0.908  0.292  1.316  2.497  Economic  Federal spending - public schools  0.859  1.198  3.706  —  —  —  —  Economic  Govt handle economy OR free market can handle  0.851  1.050  —  —  —  —  —  Economic  Federal spending - AIDS research/fight AIDS  0.773  0.671  2.896  —  —  —  —  Economic  Government health insurance scale  0.703  −1.589  −0.858  −0.170  0.840  1.660  2.604  Economic  Federal spending - Fin aid for college students  0.699  0.115  2.641  —  —  —  —  Economic  Federal spending - Social security  0.644  0.489  3.621  —  —  —  —  Economic  Federal spending - Environment  0.638  0.274  3.070  —  —  —  —  Civil rights  Government ensure fair jobs for Blacks  1.290  0.524  —  —  —  —  —  Civil rights  Blacks gotten less than they deserve  1.146  −3.173  −1.128  0.106  2.028  —  —  Civil rights  Civil rights pushes too fast or not fast enough  1.040  −2.317  1.447  —  —  —  —  Civil rights  Blacks should not have special favors to succeed  1.032  −3.512  −1.878  −0.976  0.857  —  —  Civil rights  Aid to Blacks/minorities scale (self-placement)  1.000  −3.168  −2.422  −1.501  0.127  1.035  2.075  Civil rights  Conditions make it difficult for Blacks to succeed  0.934  −2.099  0.000  0.599  2.083  —  —  Civil rights  Affirmative action in hiring/promotion  0.926  −2.409  −1.692  −0.411  —  —  —  Civil rights  Blacks must try harder to succeed  0.897  −2.745  −1.083  −0.245  1.549  —  —  Civil rights  We have gone too far pushing equal rights  0.890  −1.709  −0.374  0.426  2.183  —  —  Civil rights  Government ensure school integration  0.841  0.003  —  —  —  —  —  Civil rights  Big problem that not everyone has equal chance  0.782  −1.384  0.263  0.964  2.707  —  —  Civil rights  Should worry less about how equal people are  0.776  −1.857  −0.460  0.314  1.932  —  —  Civil rights  US fewer problems if everyone treated equally  0.670  −0.739  0.898  1.715  3.332  —  —  Civil rights  Not big problem if some have more chances  0.589  −1.373  0.099  0.967  2.785  —  —  Civil rights  Society ensure equal opportunity to succeed  0.518  0.550  2.225  2.888  4.173  —  —  Civil rights  How much has the position of Blacks changed  0.508  −1.622  0.717  —  —  —  —  Moral  Should gays/lesbians be able to adopt children  2.706  −0.770  —  —  —  —  —  Moral  Favor/oppose gays in military  1.783  −0.303  1.133  1.655  —  —  —  Moral  Newer lifestyles contribute to society breakdown  1.691  −3.632  −2.141  −1.090  0.924  —  —  Moral  Law against homosexual discrimination  1.589  −0.569  0.763  1.619  —  —  —  Moral  Should be more emphasis on traditional values  1.564  −4.572  −3.028  −1.930  −0.017  —  —  Moral  Tolerance of different moral standards  1.303  −1.619  0.463  1.327  2.802  —  —  Moral  Women equal role scale  1.130  0.110  0.880  1.338  2.422  3.060  3.705  Moral  By law, when should abortion be allowed  1.000  −0.433  0.327  2.195  —  —  —  Moral  Should adjust view of moral behavior to changes  0.987  −2.029  −0.276  0.197  1.309  —  —  Moral  When should school prayer be allowed  0.613  −1.991  0.706  2.365  —  —  —  Dimension  Variable  Disc.Param.  Cut 1  Cut 2  Cut 3  Cut 4  Cut 5  Cut 6  Economic  Federal spending - The homeless  1.346  1.252  3.981  —  —  —  —  Economic  Federal spending - Poor/poor people  1.278  0.354  3.581  —  —  —  —  Economic  Federal spending - Assistance to Blacks  1.191  −1.528  1.939  —  —  —  —  Economic  Less government better OR government do more  1.167  0.707  —  —  —  —  —  Economic  Federal spending - Child care  1.077  0.468  3.224  —  —  —  —  Economic  Federal spending - Welfare programs  1.004  −1.843  0.628  —  —  —  —  Economic  Government services/spending scale  1.000  −2.688  −1.588  −0.371  1.280  2.475  3.724  Economic  Federal spending - food stamps  0.970  −1.857  1.095  —  —  —  —  Economic  Govt too involved in things OR problems require  0.928  0.506  —  —  —  —  —  Economic  Guaranteed jobs and income scale  0.879  −2.486  −1.692  −0.908  0.292  1.316  2.497  Economic  Federal spending - public schools  0.859  1.198  3.706  —  —  —  —  Economic  Govt handle economy OR free market can handle  0.851  1.050  —  —  —  —  —  Economic  Federal spending - AIDS research/fight AIDS  0.773  0.671  2.896  —  —  —  —  Economic  Government health insurance scale  0.703  −1.589  −0.858  −0.170  0.840  1.660  2.604  Economic  Federal spending - Fin aid for college students  0.699  0.115  2.641  —  —  —  —  Economic  Federal spending - Social security  0.644  0.489  3.621  —  —  —  —  Economic  Federal spending - Environment  0.638  0.274  3.070  —  —  —  —  Civil rights  Government ensure fair jobs for Blacks  1.290  0.524  —  —  —  —  —  Civil rights  Blacks gotten less than they deserve  1.146  −3.173  −1.128  0.106  2.028  —  —  Civil rights  Civil rights pushes too fast or not fast enough  1.040  −2.317  1.447  —  —  —  —  Civil rights  Blacks should not have special favors to succeed  1.032  −3.512  −1.878  −0.976  0.857  —  —  Civil rights  Aid to Blacks/minorities scale (self-placement)  1.000  −3.168  −2.422  −1.501  0.127  1.035  2.075  Civil rights  Conditions make it difficult for Blacks to succeed  0.934  −2.099  0.000  0.599  2.083  —  —  Civil rights  Affirmative action in hiring/promotion  0.926  −2.409  −1.692  −0.411  —  —  —  Civil rights  Blacks must try harder to succeed  0.897  −2.745  −1.083  −0.245  1.549  —  —  Civil rights  We have gone too far pushing equal rights  0.890  −1.709  −0.374  0.426  2.183  —  —  Civil rights  Government ensure school integration  0.841  0.003  —  —  —  —  —  Civil rights  Big problem that not everyone has equal chance  0.782  −1.384  0.263  0.964  2.707  —  —  Civil rights  Should worry less about how equal people are  0.776  −1.857  −0.460  0.314  1.932  —  —  Civil rights  US fewer problems if everyone treated equally  0.670  −0.739  0.898  1.715  3.332  —  —  Civil rights  Not big problem if some have more chances  0.589  −1.373  0.099  0.967  2.785  —  —  Civil rights  Society ensure equal opportunity to succeed  0.518  0.550  2.225  2.888  4.173  —  —  Civil rights  How much has the position of Blacks changed  0.508  −1.622  0.717  —  —  —  —  Moral  Should gays/lesbians be able to adopt children  2.706  −0.770  —  —  —  —  —  Moral  Favor/oppose gays in military  1.783  −0.303  1.133  1.655  —  —  —  Moral  Newer lifestyles contribute to society breakdown  1.691  −3.632  −2.141  −1.090  0.924  —  —  Moral  Law against homosexual discrimination  1.589  −0.569  0.763  1.619  —  —  —  Moral  Should be more emphasis on traditional values  1.564  −4.572  −3.028  −1.930  −0.017  —  —  Moral  Tolerance of different moral standards  1.303  −1.619  0.463  1.327  2.802  —  —  Moral  Women equal role scale  1.130  0.110  0.880  1.338  2.422  3.060  3.705  Moral  By law, when should abortion be allowed  1.000  −0.433  0.327  2.195  —  —  —  Moral  Should adjust view of moral behavior to changes  0.987  −2.029  −0.276  0.197  1.309  —  —  Moral  When should school prayer be allowed  0.613  −1.991  0.706  2.365  —  —  —  Year  1986  1988  1990  1992  1994  1996  1998  2000  2004  2008  2012  Obs.  2175  2034  1974  2483  1786  1714  1281  1807  1211  2321  2054  Year  1986  1988  1990  1992  1994  1996  1998  2000  2004  2008  2012  Obs.  2175  2034  1974  2483  1786  1714  1281  1807  1211  2321  2054  Note: a) The last two rows show the number of respondents that were used in the scaling procedure. b) None of the 95 percent highest posterior density intervals of the discrimination parameters include zero. Table A1. Posterior Means of Discrimination ( γk) and Cut Point ( κk,c) Parameters, Graded Response Model Results Dimension  Variable  Disc.Param.  Cut 1  Cut 2  Cut 3  Cut 4  Cut 5  Cut 6  Economic  Federal spending - The homeless  1.346  1.252  3.981  —  —  —  —  Economic  Federal spending - Poor/poor people  1.278  0.354  3.581  —  —  —  —  Economic  Federal spending - Assistance to Blacks  1.191  −1.528  1.939  —  —  —  —  Economic  Less government better OR government do more  1.167  0.707  —  —  —  —  —  Economic  Federal spending - Child care  1.077  0.468  3.224  —  —  —  —  Economic  Federal spending - Welfare programs  1.004  −1.843  0.628  —  —  —  —  Economic  Government services/spending scale  1.000  −2.688  −1.588  −0.371  1.280  2.475  3.724  Economic  Federal spending - food stamps  0.970  −1.857  1.095  —  —  —  —  Economic  Govt too involved in things OR problems require  0.928  0.506  —  —  —  —  —  Economic  Guaranteed jobs and income scale  0.879  −2.486  −1.692  −0.908  0.292  1.316  2.497  Economic  Federal spending - public schools  0.859  1.198  3.706  —  —  —  —  Economic  Govt handle economy OR free market can handle  0.851  1.050  —  —  —  —  —  Economic  Federal spending - AIDS research/fight AIDS  0.773  0.671  2.896  —  —  —  —  Economic  Government health insurance scale  0.703  −1.589  −0.858  −0.170  0.840  1.660  2.604  Economic  Federal spending - Fin aid for college students  0.699  0.115  2.641  —  —  —  —  Economic  Federal spending - Social security  0.644  0.489  3.621  —  —  —  —  Economic  Federal spending - Environment  0.638  0.274  3.070  —  —  —  —  Civil rights  Government ensure fair jobs for Blacks  1.290  0.524  —  —  —  —  —  Civil rights  Blacks gotten less than they deserve  1.146  −3.173  −1.128  0.106  2.028  —  —  Civil rights  Civil rights pushes too fast or not fast enough  1.040  −2.317  1.447  —  —  —  —  Civil rights  Blacks should not have special favors to succeed  1.032  −3.512  −1.878  −0.976  0.857  —  —  Civil rights  Aid to Blacks/minorities scale (self-placement)  1.000  −3.168  −2.422  −1.501  0.127  1.035  2.075  Civil rights  Conditions make it difficult for Blacks to succeed  0.934  −2.099  0.000  0.599  2.083  —  —  Civil rights  Affirmative action in hiring/promotion  0.926  −2.409  −1.692  −0.411  —  —  —  Civil rights  Blacks must try harder to succeed  0.897  −2.745  −1.083  −0.245  1.549  —  —  Civil rights  We have gone too far pushing equal rights  0.890  −1.709  −0.374  0.426  2.183  —  —  Civil rights  Government ensure school integration  0.841  0.003  —  —  —  —  —  Civil rights  Big problem that not everyone has equal chance  0.782  −1.384  0.263  0.964  2.707  —  —  Civil rights  Should worry less about how equal people are  0.776  −1.857  −0.460  0.314  1.932  —  —  Civil rights  US fewer problems if everyone treated equally  0.670  −0.739  0.898  1.715  3.332  —  —  Civil rights  Not big problem if some have more chances  0.589  −1.373  0.099  0.967  2.785  —  —  Civil rights  Society ensure equal opportunity to succeed  0.518  0.550  2.225  2.888  4.173  —  —  Civil rights  How much has the position of Blacks changed  0.508  −1.622  0.717  —  —  —  —  Moral  Should gays/lesbians be able to adopt children  2.706  −0.770  —  —  —  —  —  Moral  Favor/oppose gays in military  1.783  −0.303  1.133  1.655  —  —  —  Moral  Newer lifestyles contribute to society breakdown  1.691  −3.632  −2.141  −1.090  0.924  —  —  Moral  Law against homosexual discrimination  1.589  −0.569  0.763  1.619  —  —  —  Moral  Should be more emphasis on traditional values  1.564  −4.572  −3.028  −1.930  −0.017  —  —  Moral  Tolerance of different moral standards  1.303  −1.619  0.463  1.327  2.802  —  —  Moral  Women equal role scale  1.130  0.110  0.880  1.338  2.422  3.060  3.705  Moral  By law, when should abortion be allowed  1.000  −0.433  0.327  2.195  —  —  —  Moral  Should adjust view of moral behavior to changes  0.987  −2.029  −0.276  0.197  1.309  —  —  Moral  When should school prayer be allowed  0.613  −1.991  0.706  2.365  —  —  —  Dimension  Variable  Disc.Param.  Cut 1  Cut 2  Cut 3  Cut 4  Cut 5  Cut 6  Economic  Federal spending - The homeless  1.346  1.252  3.981  —  —  —  —  Economic  Federal spending - Poor/poor people  1.278  0.354  3.581  —  —  —  —  Economic  Federal spending - Assistance to Blacks  1.191  −1.528  1.939  —  —  —  —  Economic  Less government better OR government do more  1.167  0.707  —  —  —  —  —  Economic  Federal spending - Child care  1.077  0.468  3.224  —  —  —  —  Economic  Federal spending - Welfare programs  1.004  −1.843  0.628  —  —  —  —  Economic  Government services/spending scale  1.000  −2.688  −1.588  −0.371  1.280  2.475  3.724  Economic  Federal spending - food stamps  0.970  −1.857  1.095  —  —  —  —  Economic  Govt too involved in things OR problems require  0.928  0.506  —  —  —  —  —  Economic  Guaranteed jobs and income scale  0.879  −2.486  −1.692  −0.908  0.292  1.316  2.497  Economic  Federal spending - public schools  0.859  1.198  3.706  —  —  —  —  Economic  Govt handle economy OR free market can handle  0.851  1.050  —  —  —  —  —  Economic  Federal spending - AIDS research/fight AIDS  0.773  0.671  2.896  —  —  —  —  Economic  Government health insurance scale  0.703  −1.589  −0.858  −0.170  0.840  1.660  2.604  Economic  Federal spending - Fin aid for college students  0.699  0.115  2.641  —  —  —  —  Economic  Federal spending - Social security  0.644  0.489  3.621  —  —  —  —  Economic  Federal spending - Environment  0.638  0.274  3.070  —  —  —  —  Civil rights  Government ensure fair jobs for Blacks  1.290  0.524  —  —  —  —  —  Civil rights  Blacks gotten less than they deserve  1.146  −3.173  −1.128  0.106  2.028  —  —  Civil rights  Civil rights pushes too fast or not fast enough  1.040  −2.317  1.447  —  —  —  —  Civil rights  Blacks should not have special favors to succeed  1.032  −3.512  −1.878  −0.976  0.857  —  —  Civil rights  Aid to Blacks/minorities scale (self-placement)  1.000  −3.168  −2.422  −1.501  0.127  1.035  2.075  Civil rights  Conditions make it difficult for Blacks to succeed  0.934  −2.099  0.000  0.599  2.083  —  —  Civil rights  Affirmative action in hiring/promotion  0.926  −2.409  −1.692  −0.411  —  —  —  Civil rights  Blacks must try harder to succeed  0.897  −2.745  −1.083  −0.245  1.549  —  —  Civil rights  We have gone too far pushing equal rights  0.890  −1.709  −0.374  0.426  2.183  —  —  Civil rights  Government ensure school integration  0.841  0.003  —  —  —  —  —  Civil rights  Big problem that not everyone has equal chance  0.782  −1.384  0.263  0.964  2.707  —  —  Civil rights  Should worry less about how equal people are  0.776  −1.857  −0.460  0.314  1.932  —  —  Civil rights  US fewer problems if everyone treated equally  0.670  −0.739  0.898  1.715  3.332  —  —  Civil rights  Not big problem if some have more chances  0.589  −1.373  0.099  0.967  2.785  —  —  Civil rights  Society ensure equal opportunity to succeed  0.518  0.550  2.225  2.888  4.173  —  —  Civil rights  How much has the position of Blacks changed  0.508  −1.622  0.717  —  —  —  —  Moral  Should gays/lesbians be able to adopt children  2.706  −0.770  —  —  —  —  —  Moral  Favor/oppose gays in military  1.783  −0.303  1.133  1.655  —  —  —  Moral  Newer lifestyles contribute to society breakdown  1.691  −3.632  −2.141  −1.090  0.924  —  —  Moral  Law against homosexual discrimination  1.589  −0.569  0.763  1.619  —  —  —  Moral  Should be more emphasis on traditional values  1.564  −4.572  −3.028  −1.930  −0.017  —  —  Moral  Tolerance of different moral standards  1.303  −1.619  0.463  1.327  2.802  —  —  Moral  Women equal role scale  1.130  0.110  0.880  1.338  2.422  3.060  3.705  Moral  By law, when should abortion be allowed  1.000  −0.433  0.327  2.195  —  —  —  Moral  Should adjust view of moral behavior to changes  0.987  −2.029  −0.276  0.197  1.309  —  —  Moral  When should school prayer be allowed  0.613  −1.991  0.706  2.365  —  —  —  Year  1986  1988  1990  1992  1994  1996  1998  2000  2004  2008  2012  Obs.  2175  2034  1974  2483  1786  1714  1281  1807  1211  2321  2054  Year  1986  1988  1990  1992  1994  1996  1998  2000  2004  2008  2012  Obs.  2175  2034  1974  2483  1786  1714  1281  1807  1211  2321  2054  Note: a) The last two rows show the number of respondents that were used in the scaling procedure. b) None of the 95 percent highest posterior density intervals of the discrimination parameters include zero. 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Napier. 2009. “ Political Ideology: Its Structure, Functions, and Elective Affinities.” Annual Review of Psychology  60: 307– 37. Google Scholar CrossRef Search ADS PubMed  King, Gary, Christopher J L Murray, Joshua A. Salomon, and Ajay Tandon. 2004. “ Enhancing the Validity and Cross-Cultural Comparability of Measurement in Survey Research.” American Political Science Review  98: 191– 207. Google Scholar CrossRef Search ADS   Layman, Geoffrey C., and Thomas M. Carsey. 2002. “ Party Polarization and ‘Conflict Extension’ in the American Electorate.” American Journal of Political Science  46: 786– 802. Google Scholar CrossRef Search ADS   Layman, Geoffrey C., Thomas M. Carsey, and Juliana Menasce Horowitz. 2006. “ Party Polarization in American Politics: Characteristics, Causes, and Consequences.” Annual Review of Political Science  9: 83– 110. Google Scholar CrossRef Search ADS   Levendusky, Matthew S. 2009a. The Partisan Sort . Chicago: University of Chicago Press. 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Miller, Alan S. 1992. “ Are Self-Proclaimed Conservatives Really Conservative? Trends in Attitudes and Self-Identification among the Young.” Social Forces  71: 195– 210. Google Scholar CrossRef Search ADS   Palfrey, Thomas R., and Keith T. Poole. 1987. “ The Relationship between Information, Ideology, and Voting Behavior.” American Journal of Political Science  31: 511– 30. Google Scholar CrossRef Search ADS   Perrin, Andrew J., J. Micah Roos, and Gordon W. Gauchat. 2014. “ From Coalition to Constraint: Modes of Thought in Contemporary American Conservatism.” Sociological Forum  29: 285– 300. Google Scholar CrossRef Search ADS   Poole, Keith T., and Howard L. Rosenthal. 2007. Ideology and Congress . New Brunswick, NJ: Transaction Publishers. Popp, Elizabeth, and Thomas J. Rudolph. 2011. “ A tale of Two Ideologies: Explaining Public Support for Economic Interventions.” Journal of Politics  73: 808– 20. Google Scholar CrossRef Search ADS   Ruscio, John, and Walter Kaczetow. 2008. “ Simulating Multivariate Nonnormal Data Using an Iterative Algorithm.” Multivariate Behavioral Research  43: 355– 81. Google Scholar CrossRef Search ADS PubMed  Samejima, Fumiko. 1969. “Estimation of Latent Ability Using a Response Pattern of Graded Scores.” Psychometrika Monograph Supplement. Schattschneider, Elmer E. 1960. The Semisovereign People . New York, NY: Holt, Rinehart and Winston. Schmid, Friedrich, and Axel Schmidt. 2006. “ Nonparametric Estimation of the Coefficient of Overlapping—Theory and Empirical Application.” Computational Statistics & Data Analysis  50: 1583– 96. Google Scholar CrossRef Search ADS   Sundquist, James L. 1983. Dynamics of the Party System . Washington, DC: Brookings Inst. Stimson, James A. 2004. Tides of Consent . Cambridge: Cambridge University Press. Google Scholar CrossRef Search ADS   Treier, Shawn, and Sunshine Hillygus. 2009. “ The Nature of Political Ideology in the Contemporary Electorate.” Public Opinion Quarterly  73: 679– 703. Google Scholar CrossRef Search ADS   Zaller, John. 1992. The Nature and Origins of Mass Opinion . Cambridge: Cambridge University Press. Google Scholar CrossRef Search ADS   Author notes I am grateful to Delia Baldassarri, Ned Crowley, Paul DiMaggio, Mike Hout, Daphna Harel, Colin Jerolmack, Byungkyu Lee, Jeff Manza, Adaner Usmani, and the anonymous Social Forces reviewers for their invaluable suggestions and comments. I thank also Shang E. Ha, Erez Marantz, and Howard Rosenthal for their encouragement and comments on an early draft of the paper. All remaining errors are my own. © The Author(s) 2017. Published by Oxford University Press on behalf of the University of North Carolina at Chapel Hill. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com. 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How Are We Apart? Continuity and Change in the Structure of Ideological Disagreement in the American Public, 1980–2012

Social Forces , Volume Advance Article (4) – Dec 28, 2017

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Abstract

Abstract Even after two decades of intense research, social scientists are still in disagreement over whether the American public is polarized. Starting from the premise that disagreement is multifaceted, this paper attempts to clarify how and which aspects of ideological disagreement have changed over the past few decades. Three major structural features of ideological disagreement that have been discussed under the umbrella term “polarization” are identified from the literature—polarization, partisan sorting, and dimensional alignment—and redefined into analytically distinct and non-overlapping concepts. Two different scaling methods are applied to the American National Election Studies from 1980 to 2012 in order to examine changes in how citizens organize their attitudes regarding concrete political and social issues (operational ideology) and their self-identifications with the ideological labels “liberal” and “conservative” (symbolic ideology). Results show at best mixed evidence of growing polarization. Partisan sorting has increased over time on both symbolic and operational ideology. However, it is mainly the symbolic side on which disagreement across partisan lines is most pronounced. Finally, contrary to the popular notion of a culture war dividing the United States, the public has become less polarized on moral issues, and the moral dimension of citizens’ operational ideology has become dealigned from the economic and civil rights dimension over the past decade. Introduction Two decades have passed since DiMaggio, Evans, and Bryson (1996) drew the attention of social scientists to the phenomenon of mass polarization. Their paper marked the beginning of a heated scholarly debate over whether the American public is polarized that involved not only political sociologists but also political scientists, economists, and social psychologists. However, even after twenty years of intense interdisciplinary research on the topic, there remains widespread disagreement about the phenomenon. While most social scientists agree that polarization in the US Congress has grown over the past fifty years (Bonica 2014; McCarty, Poole, and Rosenthal 2006; Poole and Rosenthal 2007), views regarding the general public differ greatly. One camp argues that citizens have become more polarized in recent decades (Abramowitz and Saunders 2008; Campbell 2016; Jacoby 2014; Layman, Carsey, and Horowitz 2006), while other scholars claim that the public has remained relatively stable in their issue preferences (Ansolabehere, Rodden, and Snyder 2006; Fiorina, Abrams, and Pope 2011; Levendusky 2009a), or even shows more consensus on several issues (Evans 2003; Fischer and Hout 2006). One reason for the conflicting views is that ideological disagreement can be structured in a variety of ways. And, depending on which of these configurations is perceived as the distinguishing feature of political disagreement, different conclusions might be reached regarding the state of public opinion. To complicate matters further, numerous studies on political polarization tend to conflate different forms of disagreement with one another, both conceptually and empirically. Hence, the precise implications of existing empirical findings remain often ambiguous. This paper attempts to clarify how and what aspects of ideological disagreement have changed since the 1980s. For this purpose, three major structural features of ideological disagreement that have been discussed under the umbrella term “polarization” are identified from the literature—polarization, partisan sorting, and dimensional alignment—and redefined into analytically distinct and mutually exclusive concepts. Admittedly, the three features do not exhaust all possibilities of how ideological disagreement might be structured. Nevertheless, they have not been integrated and compared in a longitudinal study in any of the recent contributions. While DiMaggio, Evans, and Bryson (1996) laid the groundwork for subsequent research, few have taken up their multidimensional conceptualization of political disagreement. In particular, most previous studies have focused exclusively on polarization and partisan sorting, leaving the dimensional alignment aspect relatively understudied (for a review, see Fiorina and Abrams [2008]; Fischer and Mattson [2009]; Hetherington [2009]; Layman, Carsey, and Horowitz [2006]). Yet, it is not only the disagreement on each ideological dimension per se but also how well these dimensions are aligned with one another that determines the disagreement within society as a whole. While disagreement that is tightly aligned across different ideological dimensions has the tendency to amplify political hostility, cross-cutting lines of disagreement are likely to buffer, rather than reinforce, the tension of each dimension by scattering the foci of conflict (Blau and Schwartz 1984; Coser 1956; Schattschneider 1960). Thus, any approach to the study of political disagreement that considers each ideological dimension in isolation remains necessarily incomplete. Furthermore, it is particularly the alignment of issue preferences that has undergone unexpected changes over the past decade. In this paper, I document how the three features of ideological disagreement have changed from the 1980s onward. I apply two different scaling methods to the American National Election Studies to estimate the operational and symbolic ideology of the public, where the former pertains to how citizens organize their preferences on concrete political or social issues and the latter to how they self-identify with the labels “liberal” and “conservative” (Ellis and Stimson 2012). Based on these estimates, changes in ideological disagreement are traced from 1980 to 2012. The results of the analysis show that ideological disagreement is surprisingly limited on the operational side of ideology: the ideological distributions remain largely unimodal on all dimensions, and even the divide between Democrats and Republicans is rather modest in most of the analyzed years. It is mainly the symbolic side on which partisans tend to disagree with each other. Also, I find that the moral dimension of operational ideology has depolarized and become dealigned from the economic and civil rights dimension over the past decade. Hence, the moral dimension is “cross-cutting,” rather than reinforcing, the political conflict on the traditional ideological cleavages today, thereby preventing a clear-cut bifurcation of the ideological space into two coherently opposing camps. The paper unfolds as follows. The next section defines the three disagreement concepts that will be used throughout the paper. The subsequent section presents the data and the statistical models through which the ideological disagreement of the American public will be studied. After presenting the empirical results, the paper concludes by discussing the implications of the findings. Three Ways to Disagree There is at best a weak consensus regarding the concept of polarization and how it should be measured (Hetherington 2009). While some scholars define polarization as the growing difference in political views of Democrats and Republicans (Abramowitz and Saunders 2008), others emphasize that the major characteristic of a polarized public is the bimodality of the ideological distribution (Fiorina and Abrams 2008). Still others conceptualize polarization as a property of the interrelationship between issue dimensions rather than single issues (Baldassarri and Gelman 2008; DiMaggio, Evans, Bryson 1996). Given these complexities, I start by defining three analytically distinct and mutually exclusive concepts—polarization, sorting, and dimensional alignment—which will be used to analyze how ideological disagreement is structured in the United States. Polarization and Sorting When considering a unidimensional ideological space at a specific point in time, I refer to polarization as the degree to which the ideology of the public is clustered around two separate ideological centers and how dispersed the distribution is. What is important for polarization is how far apart citizens’ positions are from one another and whether these positions are concentrated around different points. Thus, polarization is regarded as a characteristic of the shape of the overall ideological distribution. Further, polarization entails two different components that might vary independently from each other: bimodality and dispersion (DiMaggio, Evans, and Bryson 1996). The distribution of an ideological dimension might have a high variance while the shape of the distribution remains unimodal; on the other hand, the distribution can have two well-separated modes (peaks) that lie close to each other. Of course, polarization is not a binary state: a public might be more or less polarized. However, it is mainly when bimodality is combined with a high variance that we might speak of a polarized public with confidence (Fiorina and Abrams 2008). In contrast to polarization, partisan sorting is defined as the degree to which the ideology of Democrats and Republicans do not overlap with each other. It is thus a concept that captures the bivariate relationship between opinion and group membership. When all Democrats are to the left (or the right) of all Republicans, sorting is complete. If some Democrats are more conservative (or liberal) than some Republicans, sorting becomes a matter of degree. To the extent that partisanship forms a social identity (Campbell et al. 1960; Green et al. 2004), partisan sorting will mobilize more intense emotions into the political sphere as political disagreement becomes not simply about what is right or wrong but about whether “we, as a team,” are right or wrong. The consolidation of ideology and partisan identities, thus, tends to increase out-group biases and antagonism between partisan camps (Blau and Schwartz 1984; Mason 2016). Indeed, recent research has shown that hostility across partisan lines has increased over the past decades (Iyengar and Westwood 2014; Iyengar, Sood, and Lelkes 2012), and that better-sorted partisans hold more antagonistic views toward the opposing camp (Mason 2015). Polarization and sorting, as defined above, are analytically distinct concepts. Contrary to arguments that it is “logically impossible” for a perfectly sorted citizenry “not to be highly polarized” (Campbell 2016, 122), partisan sorting has, a priori, no logical implications for polarization as long as the ideological distribution of the public has at least some variability. The hypothetical distributions in figure 1 illustrate the point. The shaded area in light gray represents the overall (or marginal) ideological distribution, and the dashed black and gray lines, respectively, show the distributions of Democrats and Republicans. As we move from panel I of the figure to panel II, all Republicans change their place with Democrats who were placed to their right, so that the two groups are perfectly sorted in the latter situation. However, as the overall distribution remains unchanged, we have no increase in polarization. On the other hand, the overall distribution becomes polarized—that is, the bimodality and variance increases—as we move from panel I to panel III; yet, since the ideology of the Democrats and Republicans overlap perfectly in both cases, there is no sorting at all. This hypothetical example makes clear that an increase in sorting does not imply that polarization increases as well, and that polarization might occur without sorting. Further, it shows that conventional measurements of polarization, such as the mean difference between Democrats and Republicans, obscures the distinction between polarization and sorting: an increased mean difference between the parties may be due to sorting (a movement from panel I to II) or sorting and polarization (panel I to IV). Indeed, the difference in mean opinion might even decrease while the overall distribution becomes more polarized (panel II to III). Although the last pattern is unlikely to be observed in reality, it demonstrates how the mean differences of partisan camps can give a misleading picture of the state of disagreement. Figure 1. View largeDownload slide Four hypothetical distributions that demonstrate the difference between polarization and sorting Note: The shaded area in light gray represents the (marginal) ideological distribution of the population. Black and dark gray dashed lines and ticks represent the distribution of two subgroups of the population. Figure 1. View largeDownload slide Four hypothetical distributions that demonstrate the difference between polarization and sorting Note: The shaded area in light gray represents the (marginal) ideological distribution of the population. Black and dark gray dashed lines and ticks represent the distribution of two subgroups of the population. The definition of polarization presented here is the same as what DiMaggio, Evans, and Bryson (1996) referred to as a form of “within-population polarization” and Fiorina and Abrams (2008) as simply “polarization.” The definition of partisan sorting, on the other hand, diverges slightly from the previous literature. Increased sorting has been defined as the increase in the “correlation between” or “alignment of” partisanship and ideology, where alignment means that citizens take the same side on political issues as their parties in Congress (Levendusky 2009a, 3, 44). The definition proposed in this paper—as the lack of overlap—seems to be similar, but can lead to different conclusions in certain circumstances. For example, if sorting is defined with reference to elites, a problem arises when partisans in the public become better separated from each other, while moving in different directions than their counterparts in Congress (see, for example, Baldassarri and Park 2016; Fiorina and Levendusky 2006); on the other hand, if sorting is defined as the correlation of partisanship and ideology in the mass public, it depends partly on how extreme the ideology of the partisan groups are and, thus, conflates an aspect of polarization with sorting.1 When sorting is defined as the lack of overlap, both ambiguities are overcome: it is independent of the extremity and bimodality in ideology, and thus of what we have called polarization, and does not depend on the behavior of elites. Dimensional Alignment So far, we have implicitly assumed that the ideological space is unidimensional. However, early accounts of ideology in the United States as well as more recent research suggest that the belief system of the American public consists of at least two dimensions (Baldassarri and Goldberg 2014; Carmines, Ensley, and Wagner 2012; Layman and Carsey 2002; Lipset 1960; Treier and Hillygus 2009). The main reason for examining a multidimensional opinion space is not only because it is realistic; more importantly, it brings to the fore a new configurational aspect of disagreement that is absent in the unidimensional case—namely, the interrelationship between the dimensions on which ideology is formed. A precondition for a society to polarize into two ideologically coherent and opposing camps is that the dimensions on which ideology is formed are aligned with one another (Coser 1956; Schattschneider 1960). In the absence of alignment, the disagreement in society will remain unorganized in the sense that groups that disagree on one dimension would be equally likely to agree or disagree on other dimensions. In this case, disagreement across dimensions are “cross-cutting” one another, which prevents the concentration of “foci” (Feld 1981) of dissent. It is only when the dimensions are highly aligned that a single dimension emerges that summarizes all the disagreement in society and that two consistently opposing subgroups can form (Baldassarri and Gelman 2008). Thus, the alignment of dimensions is an indispensable element in describing how political disagreement is structured in society. Despite its importance, however, it has remained relatively understudied compared to polarization and partisan sorting, which led to the neglect of significant changes in ideological disagreement. Empirically, the concept of dimensional alignment is captured by the correlation between ideological dimensions. On the micro level, a high correlation implies that the political views of individuals show high constraint (Converse 1964); the macro-level analogue is a low level of “cross-cuttingness” between the dimensions (Lipset 1960). Note, however, that dimensional alignment is not a form of disagreement per se. Even if the ideological dimensions are highly correlated—and reduced to a single dimension—the distribution on that continuum might be centered around a single point with low variance instead of being bimodal with high variance. Rather, the correlation shapes the coherence of the belief system and, thereby, how polarization (or the lack of it) on each ideological dimension is combined to form the overall structure of polarization in society. To illustrate the point, imagine a society in which ideology has two dimensions, an economic and a social one. If the distribution on the economic dimension has a bimodal shape and the social dimension is unimodal, the joint distribution will be in general bimodal. However, with low-dimensional alignment, the subgroups thus formed will not be in consistent opposition. That is, approximately half of the members of the economically “conservative” camp will be socially “liberal,” and the same is true for the economically liberal group. Hence, in the absence of dimensional alignment, there will be an ideological dimension on which the otherwise polarized subgroups can find common ground. Furthermore, the consensus on the social dimension will “cut through” the dissent on the economic dimension and might buffer otherwise intense conflict. The way in which dimensional alignment shapes the structure of polarization in a multidimensional belief space is starkly demonstrated in the case where the ideological distribution on all dimensions is bimodal. Figure 2 shows 5,000 simulated samples from two bimodal distributions with correlation set to ρ = 0,0.3,0.6,0.9. Note that for each graph, the marginal distributions—shown as histograms at the margins of each plot—are polarized and look approximately the same. It is only the correlation between the dimensions that changes. Panel (a) of figure 2 shows the joint distribution where economic and social dimensions are uncorrelated. Although the citizens are polarized on each dimension, the disagreement of each is cross-cutting the other, so that four subgroups emerge instead of two. Also, approximately half of the hypothetical society is holding “inconsistent” opinions by being liberal on one dimension and conservative on the other. With an increase in the correlation between the dimensions, however, the number of inconsistent citizens is reduced as they are absorbed into the ideologically coherent camps. Finally, with a correlation of ρ = 0.9, we see that two large subgroups with coherently opposing views emerge, and that the ideological space can be summarized on the 45-degree line. Figure 2. View largeDownload slide Correlations and cross-cuttingness: four hypothetical distributions Note: The histograms at the margin of each panel show the marginal distributions of the two dimensions. Random draws are generated by sampling from correlated two-component normal mixture distributions using an iterative, trial-and-error algorithm proposed by Ruscio and Kaczetow (2008). Figure 2. View largeDownload slide Correlations and cross-cuttingness: four hypothetical distributions Note: The histograms at the margin of each panel show the marginal distributions of the two dimensions. Random draws are generated by sampling from correlated two-component normal mixture distributions using an iterative, trial-and-error algorithm proposed by Ruscio and Kaczetow (2008). What this simulation demonstrates is the following: only with high-dimensional alignment will polarization on each dimension lead to a polarized society. Indeed, even if ideology is highly polarized on all dimensions, 2D subgroups will form out of a D-dimensional belief space as long as the inter-dimension correlation remains sufficiently low. Society would be “fragmented” rather than polarized with low-dimensional alignment: clusters of citizens occupying distinct positions in the ideological space would emerge, but they would be in agreement on several ideological dimensions, rather than coherently contradicting one another. Therefore, although dimensional alignment is not a form of polarization per se, it determines the shape of the overall (or joint) ideological distribution in society, enabling or preventing the bifurcation of the public into two camps with consistently opposing views. Operational versus Symbolic Ideology While the term “ideology” has been defined in numerous ways (Gerring 1997; Jost, Federico, and Napier 2009), in this paper I focus on two different meanings that have been attached to the concept by scholars and pundits: namely, how citizens identify themselves with the labels “liberal” and “conservative,” and how they organize their beliefs regarding concrete political issues. Following Ellis and Stimson (2012), I refer to the former aspect as symbolic ideology and to the latter as operational ideology. It has long been thought that self-identification with liberal or conservative labels is only moderately related to concrete policy preferences (Conover and Feldman 1981; Free and Cantril 1967; Miller 1992). Indeed, in the aggregate, operational and symbolic ideology seem to contradict each other: if American citizens are asked about their self-identification, the majority identify with the conservative label; on the other hand, when asked about specific issues and policies, they tend to be “liberal” in the sense that they want more public spending, a bigger government, and more equal treatment of minorities (Stimson 2004). More important than the aggregate trends per se is that many citizens base their ideological self-identification and their issue preferences on systematically different foundations (Popp and Rudolph 2011). Some citizens associate the terms “liberal” and “conservative” with their preferences regarding the size of government; for others, however, the reason for identifying with these labels stems from their non-political connotations (Conover and Feldman 1981; Ellis and Stimson 2012).2 The distinct foundations of symbolic and operational ideology suggest that disagreement on these two “faces” of ideology might be structured in a different way. However, there has been little effort to systematically compare changes in ideological disagreement across these two sides of ideology. Most polarization scholars focus exclusively on only one of the two aspects or draw no clear distinction between symbolic and operational ideology. In some instances, measures of operational and symbolic ideology are even combined into unidimensional composite scales (e.g., Abramowitz 2010; Levendusky 2009b). Not only does this practice blur the distinction between symbolic and operational ideology but, given that operational ideology is multidimensional, it is not clear to which operational dimension the self-identification aspect belongs (Carmines, Ensley, and Wagner 2012). Therefore, in what follows, I treat the two faces of ideology separately. Data and Methods The data that are analyzed in this paper come from the American National Election Studies Time Series (ANES). Any study that tries to make comparisons across subgroups or over time with survey respondents has to address the problem of comparability. This problem is especially acute in the case of estimating latent traits, such as ideology. Since a latent variable has no natural scale, it is standard practice to normalize it to have mean zero and variance one. However, this renders the recovered latent dimension incomparable across time, unless all periods under study are scaled jointly.3 For this reason, I introduce two different scaling methods—one for operational and the other for symbolic ideology—that place all estimated ideological positions on a common scale and, thus, makes them comparable across different years. Estimation of Operational Ideology For the analysis of operational ideology, I use all political attitude measures in the ANES that meet two criteria. First, to prevent cherry-picking items that might bias the results of the analysis, I use all issues in the ANES that were administrated at least three times between 1986 and 2012. The restriction on the period is necessary because most of the moral issues that sparked the debate over the “culture war” (Fiorina, Abrams, and Pope 2011; Hunter and Wolfe 2006) are not measured before 1986. Second, I include only attitude measures that pertain to economic, civil rights, and moral issues. The items are classified following the typology in Baldassarri and Goldberg (2014). However, in this paper I do not analyze issues that belong to their foreign policy/security category, as these issues have shown rather idiosyncratic patterns in previous studies (Baldassarri and Gelman 2008; Hurwitz and Peffley 1987). The selection process leaves me with 43 items. I include all respondents that answered at least one of the attitude questions in the analysis. The list of items analyzed, their classification, and the sample sizes for each year are shown in the  appendix. To estimate the operational ideology of the respondents, I use a graded response model (GRM) (Samejima 1969). As in factor analysis, the GRM uses observed responses on a set of items to recover positions in a latent space (i.e., “factor scores”). Differently from the linear factor model, however, the GRM assumes that each item is measured on a binary or ordinal scale and uses logistic link functions to relate the latent dimensions to the responses. Thus, the GRM overcomes the unrealistic assumption of the usual factor model that the association of the latent trait and the observed responses is linear and that all observed variables are measured on a continuous scale. I use a Bayesian approach to estimate the model out of practical rather than philosophical reasons. Most importantly, by estimating the model using MCMC techniques, natural uncertainty estimates of the latent positions (and any function thereof) are easily obtained, which is not the case when the model is fit by maximum likelihood. I use weakly informative priors for all parameters in the model. To identify the latent scale, I fix the prior mean of each latent dimension in the first year of the analysis to zero and fix one discrimination parameter for each latent dimension equal to one.4 Also, as in confirmatory factor analysis, I do not allow for cross-loadings in most of the models. All inference is drawn by sampling from the joint posterior distribution of the parameters using a Hamiltonian Monte Carlo algorithm (the No-U-Turn Sampler) implemented in STAN. For each specification of the model, I run six independent chains with 15,000 iterations. The first 10,000 iterations of each chain are discarded as “burn-in,” and inference is drawn from the remaining 5,000 iterations, which are sampled with a thinning interval of 20. The traceplots of all models that are presented below showed strong signs of convergence, with the potential scale reduction factor, Rˆ (Gelman et al. 2014, ch. 11), being estimated to be below 1.05 for all parameters in all models. Convergence statistics and posterior predictive checks for the final model, as well as details on model specification and estimation, can be found in online appendix A. Estimation of Symbolic Ideology The analysis of symbolic ideology appears to be much simpler, as the ANES includes a direct measurement of it: namely, the seven-point liberal-conservative self-placement item. A potential threat to the direct analysis of the item is that the response categories—“extremely liberal” to “extremely conservative”—might have different meanings for different respondents (Aldrich and McKelvey 1977; Levendusky 2009b), a problem known as differential item functioning (Hare et al. 2015). In their path-breaking paper, Aldrich and McKelvey (1977) proposed a method to correct differential item functioning (DIF) of the seven-point liberal-conservative item, which is similar to the “anchoring vignette” approach of King et al. (2004). The basic idea behind the Aldrich-McKelvey (A-M) scaling is to assume that the political stimuli—that is, politicians and political parties—have fixed position on a unidimensional latent scale, so that the positions of the respondents can be evaluated relative to these fixed points. For example, if respondent i states that she is “moderate” but places Barack Obama and Mitt Romney, respectively, in the “slightly conservative” and “extremely conservative” category, she would be estimated to be more liberal than respondent j, who says that he is “extremely liberal” but places Obama into the same “extremely liberal” category and Mitt Romney into the “liberal” category. Since respondents are asked in each year of the ANES to place not only themselves but also several political stimuli on the same seven-point liberal-conservative scale, it is possible to infer the position of each respondent relative to the fixed stimuli positions. Further, as these “corrected” positions of the respondents are all evaluated relative to the same set of stimuli, they lie on a common scale and are therefore comparable. In a recent analysis, Hare et al. (2015) applied a Bayesian version of A-M scaling to the ANES, and found that the electorate is more polarized than the (unscaled) raw responses suggest. The analysis was, however, restricted to a single year, namely 2012. One of the reasons for the restriction lies in the limitation of the method in estimating a common scale on which all corrected positions can be placed over time. To overcome this “bridging” problem, I project the responses on the seven-point liberal-conservative item into a scale that satisfies two conditions: (1) it approximately measures the same liberal-conservative dimension on which the respondents are asked to place the stimuli (and themselves); and (2) it remains constant over the entire period of the study. An obvious candidate for such a scale is the first dimension of the Common Space DW-NOMINATE scores (Poole and Rosenthal 2007). The DW-NOMINATE scores measure the ideology of legislators by scaling their roll-call voting patterns and are widely regarded as the standard ideological measure of members of Congress. The first dimension of the DW-NOMINATE scores is typically interpreted as the liberal-conservative dimension, while the second dimension measures a racial/regional dimension. Importantly, the explanatory power of the second dimension has rapidly declined in the late 1970s, so that, from the 1980s onward, ideology in Congress is regarded as unidimensional and only the first dimension is used (Poole and Rosenthal 2007). Also, as the NOMINATE scores are estimated on the same scale across different years, they satisfy the two conditions outlined above. The projection is done as follows. First, I select all political figures who 1) served either in Congress or as president; and 2) were placed by the respondents on the seven-point liberal-conservative scale between 1980 and 2012 in the ANES. Thereafter, I regress the (first dimension) DW-NOMINATE scores of these figures, plus the median score of each party in each year, on the respondents’ placements of these stimuli. As the estimated regression coefficients reflect how respondents distort the positions of the stimuli, the linear projection of the self-placements into the NOMINATE space “corrects” for the DIF in the same way as the A-M scaling procedure. Indeed, in online appendix A, it is shown that the projection method is mathematically equivalent to A-M scaling, except that the NOMINATE scores are used to estimate the stimuli positions, whereas the original model estimates these positions from survey responses. The crucial assumption underlying this method is that the seven-point liberal-conservative item of the ANES measures approximately the same dimension as the NOMINATE scores. Fortunately, this assumption can be tested, at least indirectly. Since A-M scaling has been shown to perform well on public opinion data (Armstrong et al. 2014; Palfrey and Poole 1987), I correlate the corrected measures obtained by A-M scaling with those obtained from the projection method within each year. Also, I estimate the same projection model using CF scores, which estimate politicians’ ideology from over 100 million records of campaign finance data (Bonica 2014), in place of the NOMINATE scores as a second robustness check. A high correlation coefficient between these estimates indicates that the sets of corrected positions measure approximately the same scale up to an affine transformation. In the analysis of the symbolic ideology, I use the presidential election years from 1980 to 2012. I restrict the analysis to this period because of the following reasons. First, it is only after the late 1970s that the ideological space measured by the NOMINATE scores has become unidimensional (Poole and Rosenthal 2007). Thus, the projection method has face validity only for the post-1980 period. The restriction to the presidential election years is necessary because only one political figure (the incumbent president) is placed on the seven-point liberal-conservative scale by all respondents in congressional election years. Respondents who placed fewer than three stimuli on the seven-point liberal-conservative item or failed to place themselves on the scale were not included in the analysis. The Common Space DW-NOMINATE scores and the CF scores for available political figures over the period 1980–2012 are shown in table 1. Table 1. Common Space DW-NOMINATE Scores and CF Scores of Political Stimuli in the ANES Stimuli  NOMINATE  CF scores  Stimuli  NOMINATE  CF scores  Anderson  0.187  −0.663  Gore  −0.336  −0.894  Brown  —  −0.651  Jackson  —  −0.761  Buchanan  —  1.258  T. Kennedy  −0.460  −0.885  H. W. Bush  0.578  0.796  Kerry  −0.373  −0.956  W. Bush  0.729  0.922  McCain  0.38  0.68  Carter  −0.521  −0.38  Mondale  −0.447  −0.798  Clinton  −0.452  −0.899  Nader  —  −1.338  Connally  —  0.893  Obama  −0.368  −1.351  Dole  0.328  0.6  Perot  —  0.447  Dukakis  —  −0.824  Reagan  0.688  0.987  Ford  0.501  —  Romney  —  0.879  Stimuli  NOMINATE  CF scores  Stimuli  NOMINATE  CF scores  Anderson  0.187  −0.663  Gore  −0.336  −0.894  Brown  —  −0.651  Jackson  —  −0.761  Buchanan  —  1.258  T. Kennedy  −0.460  −0.885  H. W. Bush  0.578  0.796  Kerry  −0.373  −0.956  W. Bush  0.729  0.922  McCain  0.38  0.68  Carter  −0.521  −0.38  Mondale  −0.447  −0.798  Clinton  −0.452  −0.899  Nader  —  −1.338  Connally  —  0.893  Obama  −0.368  −1.351  Dole  0.328  0.6  Perot  —  0.447  Dukakis  —  −0.824  Reagan  0.688  0.987  Ford  0.501  —  Romney  —  0.879  Table 1. Common Space DW-NOMINATE Scores and CF Scores of Political Stimuli in the ANES Stimuli  NOMINATE  CF scores  Stimuli  NOMINATE  CF scores  Anderson  0.187  −0.663  Gore  −0.336  −0.894  Brown  —  −0.651  Jackson  —  −0.761  Buchanan  —  1.258  T. Kennedy  −0.460  −0.885  H. W. Bush  0.578  0.796  Kerry  −0.373  −0.956  W. Bush  0.729  0.922  McCain  0.38  0.68  Carter  −0.521  −0.38  Mondale  −0.447  −0.798  Clinton  −0.452  −0.899  Nader  —  −1.338  Connally  —  0.893  Obama  −0.368  −1.351  Dole  0.328  0.6  Perot  —  0.447  Dukakis  —  −0.824  Reagan  0.688  0.987  Ford  0.501  —  Romney  —  0.879  Stimuli  NOMINATE  CF scores  Stimuli  NOMINATE  CF scores  Anderson  0.187  −0.663  Gore  −0.336  −0.894  Brown  —  −0.651  Jackson  —  −0.761  Buchanan  —  1.258  T. Kennedy  −0.460  −0.885  H. W. Bush  0.578  0.796  Kerry  −0.373  −0.956  W. Bush  0.729  0.922  McCain  0.38  0.68  Carter  −0.521  −0.38  Mondale  −0.447  −0.798  Clinton  −0.452  −0.899  Nader  —  −1.338  Connally  —  0.893  Obama  −0.368  −1.351  Dole  0.328  0.6  Perot  —  0.447  Dukakis  —  −0.824  Reagan  0.688  0.987  Ford  0.501  —  Romney  —  0.879  Measurement of Disagreement To examine how polarization, as the term was defined above, has changed over time, it is necessary to consider both the bimodality and dispersion of ideological distributions. However, there seems to be no agreed-upon measure that reliably captures the bimodality of distributions, let alone both bimodality and dispersion.5 Therefore, I rely predominantly on kernel density estimators and graphical methods in examining changes in polarization. For the changes in dispersion, however, I also analyze trends in the standard deviation of each dimension. Partisan sorting is measured by the coefficient of overlapping (Schmid and Schmidt 2006; Levendusky and Pope 2011), which is defined as   OVL(X,Y)=∫min{f(x),g(x)}dx,where f and g are, respectively, the density functions for Democrats and Republicans defined over a common ideological dimension. The coefficient of overlapping measures the density of the overlapping region between two distributions. It is equal to 1 if the densities f and g overlap perfectly and 0 if the densities are defined over disjoint domains. For less extreme cases, OVL(X,Y) lies between 0 and 1. As figure 3 illustrates, the coefficient of overlapping is an ideal measure of partisan sorting, since (one minus) the coefficient corresponds to the very definition of the concept—namely, the lack of overlap between Democrats and Republicans. The coefficient is estimated with the consistent estimator   OVL^(x1,…,xn,y1,…,ym)=1n∑i=1nI{fˆ(xi)<gˆ(xi)}(xi)+1m∑j=1mI{gˆ(yj)≤fˆ(yj)}(yj),where the xi’s and yj’s are, respectively, the sample points of Democrats and Republicans, fˆ and gˆ are kernel density estimators of f and g, and IA(u) is an indicator function that is 1 if u ∈ A and 0 otherwise. Figure 3. View largeDownload slide Hypothetical distributions of Democrats, f, and Republicans, g. The coefficient of overlapping measures the overlapping region of the two distributions. Figure 3. View largeDownload slide Hypothetical distributions of Democrats, f, and Republicans, g. The coefficient of overlapping measures the overlapping region of the two distributions. Finally, the degree of dimensional alignment is measured by the Pearson correlation coefficient between ideological dimensions. As discussed above, the inter-dimension correlation reflects the degree to which one dimension can be represented as a linear transformation of the other. Hence, the closer the correlation is to one, the higher the alignment of disagreement across the dimensions. Since the projection method results in a unidimensional continuum, the analysis of dimension alignment will be restricted to the operational aspect of ideology. Results Dimensionality of Operational Ideology While ideology in Congress has become unidimensional after the 1980s (Poole and Rosenthal 2007), how many dimensions best summarize the issue preferences of citizens remains a debated topic among social scientists (Carmines, Ensley, and Wagner 2012; Jost, Federico, Napier 2009). Hence, before we can analyze how disagreement changed over time, we need to determine the number of latent dimensions that best represents the operational ideology of the public. For this task, I fit eight different models to the data and compare their fit by the Watanabe-Akaike information criterion (WAIC). The WAIC is used to compare the out-of-sample predictive accuracy of the fitted Bayesian models, with smaller values indicating a better fit of the model (Gelman et al. 2014). The results are shown in table 2. Table 2. WAIC Values for Different Model Specifications of the Graded Response Model Model  Dim  Latent dimensions  WAIC  elpd  pˆ  Mean  Var.  Corr.  Model 8  3  Y  Y  Y  1327409.78  −663704.89  41983.90  Model 7  3  C  Y  Y  1327839.23  −663919.61  42332.66  Model 6  3  C  C  Y  1327965.44  −663982.72  42391.69  Model 5  3  C  C  C  1328053.69  −664026.84  42532.59  Model 4  2  C  C  C  1338523.14  −669261.57  32125.74  Model 3  2  C  C  C  1343005.45  −671502.72  31493.66  Model 2  2  C  C  C  1349263.22  −674631.61  29975.46  Model 1  1  C  C  —  1363502.33  −681751.16  18614.27  Model  Dim  Latent dimensions  WAIC  elpd  pˆ  Mean  Var.  Corr.  Model 8  3  Y  Y  Y  1327409.78  −663704.89  41983.90  Model 7  3  C  Y  Y  1327839.23  −663919.61  42332.66  Model 6  3  C  C  Y  1327965.44  −663982.72  42391.69  Model 5  3  C  C  C  1328053.69  −664026.84  42532.59  Model 4  2  C  C  C  1338523.14  −669261.57  32125.74  Model 3  2  C  C  C  1343005.45  −671502.72  31493.66  Model 2  2  C  C  C  1349263.22  −674631.61  29975.46  Model 1  1  C  C  —  1363502.33  −681751.16  18614.27  Note: Dim = number of latent dimensions; WAIC = Watanabe-Akaike information criterion; elpd = expected log predictive density; pˆ = effective number of parameters; C = common prior for all years; Y = year-specific prior. Table 2. WAIC Values for Different Model Specifications of the Graded Response Model Model  Dim  Latent dimensions  WAIC  elpd  pˆ  Mean  Var.  Corr.  Model 8  3  Y  Y  Y  1327409.78  −663704.89  41983.90  Model 7  3  C  Y  Y  1327839.23  −663919.61  42332.66  Model 6  3  C  C  Y  1327965.44  −663982.72  42391.69  Model 5  3  C  C  C  1328053.69  −664026.84  42532.59  Model 4  2  C  C  C  1338523.14  −669261.57  32125.74  Model 3  2  C  C  C  1343005.45  −671502.72  31493.66  Model 2  2  C  C  C  1349263.22  −674631.61  29975.46  Model 1  1  C  C  —  1363502.33  −681751.16  18614.27  Model  Dim  Latent dimensions  WAIC  elpd  pˆ  Mean  Var.  Corr.  Model 8  3  Y  Y  Y  1327409.78  −663704.89  41983.90  Model 7  3  C  Y  Y  1327839.23  −663919.61  42332.66  Model 6  3  C  C  Y  1327965.44  −663982.72  42391.69  Model 5  3  C  C  C  1328053.69  −664026.84  42532.59  Model 4  2  C  C  C  1338523.14  −669261.57  32125.74  Model 3  2  C  C  C  1343005.45  −671502.72  31493.66  Model 2  2  C  C  C  1349263.22  −674631.61  29975.46  Model 1  1  C  C  —  1363502.33  −681751.16  18614.27  Note: Dim = number of latent dimensions; WAIC = Watanabe-Akaike information criterion; elpd = expected log predictive density; pˆ = effective number of parameters; C = common prior for all years; Y = year-specific prior. Model 1 fits a unidimensional model with no distinctions between economic, civil rights, and moral issues. Model 2, model 3, and model 4 are two-dimensional models, where the economic items load exclusively on one dimension and the morality items on the other dimension. The civil rights items load only on the moral dimension in model 2, load only on the economic dimension in model 3, and are allowed to load on both the economic and moral dimension in model 4. The last four models fit three-dimensional latent structures to the data, where each dimension is estimated from items pertaining to economic, civil rights, and moral issues. Model 5 estimates a single variance-covariance matrix of the latent dimensions for all years. The rest of the models relax the assumption of model 5 by estimating separate inter-dimension correlations (model 6), correlations and standard deviations (model 7), and correlations, standard deviations, and means (model 8) for each year. Table 2 shows clearly that a three-dimensional latent structure fits the data better than single- or two-dimensional ones. Model 8 has the lowest WAIC, which suggests that it fits the data best among the proposed models. Posterior predictive checks show that model 8 reproduces the observed response patterns in the data reasonably well (see online appendix A). In line with previous studies that argued that domain-specific principles guide political attitudes (e.g., Feldman and Zaller 1992; Goren 2012) and that ideology is multidimensional (Layman and Carsey 2002; Lipset 1960; Treier and Hillygus 2009), this result renders questionable the assumption that political preferences are organized on a single dimension, as it was often assumed in the study of polarization. Thus, in the following analysis of operational ideology, the three dimensions will be treated separately. Operational Ideology: Polarization, Sorting, and Dimensional Alignment How has ideological disagreement changed over time? Figure 4 shows the density of posterior means of respondents’ ideological positions on the economic, civil rights, and moral dimension. Only three years—the first (1988), middle (2000), and last (2012) presidential election year of the data—are shown in the figure for clarity. As evident from figure 4, none of the distributions has a bimodal shape. Furthermore, while it has been argued that the ideological distribution of voters is bimodal (Abramowitz 2010), I find no indication of bimodality in any of the distributions even when the sample is restricted to individuals who reported to have voted in the last election.6 Thus, when polarization is measured in terms of bimodality, we can safely conclude that the electorate is not and has not been polarized on any of the three dimensions: most citizens hold moderate, rather than extreme, issue preferences. Figure 4. View largeDownload slide Kernel density estimates of ideological distribution: operational ideology, 1988–2012 Note: Figure shows estimated distribution of posterior means. Distributions for all analyzed years are shown in online appendix A. Figure 4. View largeDownload slide Kernel density estimates of ideological distribution: operational ideology, 1988–2012 Note: Figure shows estimated distribution of posterior means. Distributions for all analyzed years are shown in online appendix A. Figure 4 indicates also that the variance of the economic and civil rights dimension has increased, while, on the moral dimension, the dispersion first increases and then decreases again. To further explore how the dispersion has changed, I plot the estimated standard deviation of each dimension from 1986 to 2012 in the first row of figure 5.7 The figure shows that it is mainly the economic dimension on which the dispersion has continuously grown. The standard deviation of the civil rights dimension increases as well, but the trend is less consistent and might be due to the unusually high variance in the last year. Figure 5. View largeDownload slide Trends in standard deviations, coefficients of overlapping, and correlations: operational ideology, 1986–2012 Note: Standard deviations, coefficients of overlapping, and correlations are calculated based on 50 posterior draws from the joint latent ideological distribution to summarize the uncertainty in the estimates. Smoothed (LOESS) time trends for each posterior draw are shown in light gray. Figure 5. View largeDownload slide Trends in standard deviations, coefficients of overlapping, and correlations: operational ideology, 1986–2012 Note: Standard deviations, coefficients of overlapping, and correlations are calculated based on 50 posterior draws from the joint latent ideological distribution to summarize the uncertainty in the estimates. Smoothed (LOESS) time trends for each posterior draw are shown in light gray. The most surprising result is found on the moral dimension. Contradicting the widely publicized rhetoric of a “culture war” (Fiorina, Abrams, and Pope 2011; Frank 2004; Hunter and Wolfe 2006; Jacoby 2014), the moral dimension is the only domain for which we can safely conclude that no polarization has occurred no matter how it is measured. Quite to the contrary, the standard deviation of the moral domain shows an inverse U-shaped pattern over time: after a rapid increase from 1988 to the mid-1990s, it has declined sharply over the past decade. In other words, in terms of the variance of the ideological distribution, citizens were less polarized on moral issues in 2012 compared to 1998. Next, we turn to partisan sorting and dimensional alignment. The second row of figure 5 shows how the overlap between the distributions of Democrats and Republicans has changed from 1986 to 2012. Consistent with existing literature on partisan sorting, the public is better sorted on all three dimensions of operational ideology compared to thirty years ago. However, it is also apparent that the absolute degree of sorting is far from perfect. Over the entire period under analysis, the ideological distributions of Democrats and Republicans overlap more than 50 percent. Thus, even though sorting has increased, there seems to be more agreement than disagreement across partisan lines. The only exception is the economic dimension in the year 2012, where Democrats and Republicans, responding to the Great Recession, moved rapidly in opposite directions on issues such as redistribution and market regulation (Brooks and Manza 2013). As with polarization, the most intriguing finding with respect to partisan sorting pertains to the moral dimension. After showing a consistent decline up to the mid-1990s, the overlap between Democrats and Republicans has remained at the same level and even shows signs of an increase over the past decade. Note also that in none of the years are citizens better sorted on the moral dimension than on the other two dimensions. Hence, it is mainly on the economic and civil rights dimension that the views of Democrats and Republicans have constantly diverged. Changes in dimensional alignment are shown in last row of figure 5. Except for the unusually high estimates in 1986, the correlation between the economic and civil rights dimension has stayed fairly stable between 0.6 and 0.7. On the other hand, the correlation between the moral dimension and the other two dimensions shows a clear inverse U-shaped pattern. This suggests that the American public has not become more constrained in its ideology. And the moral dimension, after becoming rapidly aligned with the other two dimensions from 1986 to 1996, is cross-cutting the traditional ideological divide on economic and civil rights dimension once again. In light of the simulation shown in figure 2, this suggests that the potential of the American public to become split into two coherently opposing camps has in fact decreased over the past decade. Symbolic Ideology: Polarization and Partisan Sorting As the last step of the analysis, we turn to the symbolic aspect of ideology—that is, how respondents identify themselves with the labels “liberal” and “conservative.” Table 3 presents how the scaled positions obtained from the projection into the first dimension of the DW-NOMINATE space correlate with other measures of symbolic ideology. The within-year correlations between the projected positions and those obtained from Aldrich-McKelvey scaling are extremely high. Also, the stimuli positions recovered from the A-M procedure showed a strong linear relationship with the original DW-NOMINATE scores (r = 0.929). This result is in line with previous research, which argued that the electorate holds a quite accurate view of where politicians and parties stand once DIF is accounted for (Aldrich and McKelvey 1977; Armstrong et al. 2014; Palfrey and Poole 1987).8 Table 3. Correlations of Scaled Positions Estimated by Projection into the NOMINATE Space with 1) Raw Self-Placements on the Liberal-Conservative Seven-Point Item, 2) Estimates Obtained from Aldrich-McKelvey Scaling, and 3) Estimates Obtained from Projections into the CF Score Space Year  1980  1984  1988  1992  1996  2000  2004  2008  2012  1. Raw  0.561  0.501  0.571  0.627  0.688  0.619  0.755  0.606  0.609  2. A-M  0.978  0.990  0.978  0.995  0.999  0.993  0.997  0.999  0.999  3. CF  0.926  0.994  0.859  0.908  0.935  0.958  0.924  0.990  0.916  Obs.  960  1453  1279  1677  1289  587  875  1540  1365  Year  1980  1984  1988  1992  1996  2000  2004  2008  2012  1. Raw  0.561  0.501  0.571  0.627  0.688  0.619  0.755  0.606  0.609  2. A-M  0.978  0.990  0.978  0.995  0.999  0.993  0.997  0.999  0.999  3. CF  0.926  0.994  0.859  0.908  0.935  0.958  0.924  0.990  0.916  Obs.  960  1453  1279  1677  1289  587  875  1540  1365  Note: The last row shows the number of respondents that were used in the scaling procedure. In 2000, half of the respondents were randomly assigned to the branching version of the self-placement question. These respondents were excluded from the analysis. Table 3. Correlations of Scaled Positions Estimated by Projection into the NOMINATE Space with 1) Raw Self-Placements on the Liberal-Conservative Seven-Point Item, 2) Estimates Obtained from Aldrich-McKelvey Scaling, and 3) Estimates Obtained from Projections into the CF Score Space Year  1980  1984  1988  1992  1996  2000  2004  2008  2012  1. Raw  0.561  0.501  0.571  0.627  0.688  0.619  0.755  0.606  0.609  2. A-M  0.978  0.990  0.978  0.995  0.999  0.993  0.997  0.999  0.999  3. CF  0.926  0.994  0.859  0.908  0.935  0.958  0.924  0.990  0.916  Obs.  960  1453  1279  1677  1289  587  875  1540  1365  Year  1980  1984  1988  1992  1996  2000  2004  2008  2012  1. Raw  0.561  0.501  0.571  0.627  0.688  0.619  0.755  0.606  0.609  2. A-M  0.978  0.990  0.978  0.995  0.999  0.993  0.997  0.999  0.999  3. CF  0.926  0.994  0.859  0.908  0.935  0.958  0.924  0.990  0.916  Obs.  960  1453  1279  1677  1289  587  875  1540  1365  Note: The last row shows the number of respondents that were used in the scaling procedure. In 2000, half of the respondents were randomly assigned to the branching version of the self-placement question. These respondents were excluded from the analysis. The estimated distribution of the corrected positions is shown in the first column of figure 6.9 The solid line and dashed line represent, respectively, the estimated density based on projections into the NOMINATE and CF score space. As shown in the figure, none of the estimated distributions has a bimodal shape and much of the density is concentrated at the center in each year. On the other hand, the variance of the distributions is increasing over time. Hence, similarly to the findings on the economic dimension of operational ideology, most citizens are still holding moderate views despite an increased dispersion of the ideological distribution. Again, the same conclusion also holds when the analysis is restricted to voters.10 Figure 6. View largeDownload slide Estimated distribution of symbolic ideology (left) and coefficient of overlapping (right), 1980–2012 Note: Solid and dashed lines of the density plots, respectively, represent kernel density estimates based on projections into the NOMINATE and CFscore space. A comparison between the distributions of raw and scaled self-placements are shown in online appendix B. Figure 6. View largeDownload slide Estimated distribution of symbolic ideology (left) and coefficient of overlapping (right), 1980–2012 Note: Solid and dashed lines of the density plots, respectively, represent kernel density estimates based on projections into the NOMINATE and CFscore space. A comparison between the distributions of raw and scaled self-placements are shown in online appendix B. The right panel of figure 6 shows how the overlap in the distributions of Democrats and Republicans changed. In comparison to what was found in the case of operational ideology, where the majority of the partisans overlapped in their views, partisans are much better sorted on the symbolic side. The overlap between the distributions of Democrats and Republicans has been continuously declining for both sets of corrected ideological positions. Note that this is not true when the overlap is calculated on the raw self-placements, in which case the overlap remains fairly stable after 1996. Although the general gap in the overlap coefficients between the scaled and raw estimates seems to be due to the categorical nature of the self-identification item, the divergence between the time trends from 2004 to 2012 is clearly attributable to the correction of differential item functioning. Hence, it is true that DIF problem suppresses the amount of political disagreement. In contrast to what Hare et al. (2015) argue, however, it is not polarization but sorting that the problem is suppressing. Substantively more important is the absolute degree of sorting that is observed. The estimated overlap between Republicans and Democrats dropped from 0.45 (95 percent CI: [0.41, 0.50]) in 1980 to 0.33 (95 percent CI: [0.26, 0.33]) in 2012.11 In other words, even in 1980, partisans were more in disagreement than agreement and, by 2012, only about a third of them overlapped in their symbolic ideology.12 Hence, although sorting has increased on both operational ideology and symbolic ideology, it is mainly on the symbolic side that partisans hold well-separated views. Discussion and Conclusion Over the past two decades, the dominant question that guided research on polarization has been how much, or to what extent, the American public is polarized. Even polarization and partisan sorting have been often discussed as if they pertain to the same facet of disagreement and differ only in their intensity. This paper, on the other hand, returned to questions posed at the very beginning of the polarization debate, namely the emphasis of DiMaggio, Evans, and Bryson (1996) that polarization should be thought of as a multidimensional concept. Hence, the question asked in this paper might be summarized as “how are we apart?” instead of “how far are we apart?” The empirical analysis found two opposing currents in the time trends with regard to polarization. While none of the distributions of either operational or symbolic ideology had a bimodal shape in any year, the variance has increased for symbolic ideology as well as the economic dimension of operational ideology from the 1980s onward. The different findings with respect to extremism and bimodality offer a reason for why even scholars who make a clear distinction between polarization and sorting reach different conclusions regarding how ideological disagreement has changed over the past decades. If polarization is defined in terms of the spread of the ideological distribution, there exists some evidence for polarization; if the essential characteristic of polarization is the existence of two opposing camps—and hence bimodality—evidence for polarization is at best weak if not nonexistent. The analytical distinction between the symbolic and operational aspects of ideology is demonstrated to be fruitful in the analysis as well. While most social scientists agree that the American public is better sorted nowadays, what has gone relatively unnoticed is that the absolute degree of partisan sorting is surprisingly limited on the operational side of ideology. Indeed, partisans seem to be more in agreement than disagreement across all dimensions, except for the economic dimension in 2012. On the symbolic side of ideology, the picture looks entirely different: here, we find that partisans differed significantly in their ideology even in 1988 and, by 2012, the ideological overlap between partisan camps dropped to 30 percent. Hence, the statement that partisans differ sharply in their ideology today is only valid for symbolic ideology; for the operational side of ideology, most citizens hold similar views even if their partisanship differs. This suggests that future studies on political disagreement should make a clear distinction between the two “faces” of ideology in their analysis. Finally, throughout the analysis of operational ideology, the moral dimension showed distinct time trends on all forms of disagreement. Until the late 1990s, the moral dimension became increasingly similar to the economic and civil rights dimension. Not only did the dispersion grow, but partisan sorting evidenced a rapid surge as well. Based on these symptoms, it appeared as if morality would become another axis that reinforces the conflict on the traditional ideological cleavages (Baldassarri and Gelman 2008; Layman and Carsey 2002). In analyzing additional years of the ANES, this study showed that previous accounts are only valid for the premillennial period. With the turn of the century, all previously observed trends on the moral dimension are showing signs of a reversal: the variance dropped sharply, and partisan sorting started to show signs of a decline as well. Furthermore, the moral dimension became less correlated with—and thus dealigned from—the other two dimensions of operational ideology over the past decade, a finding that has been overlooked in previous research. These findings suggest that the reports of a “culture war” are likely exaggerated. The distribution of moral ideology is not, and has not been, bimodal at any time point, partisans were never as sharply divided in their moral ideology compared to their economic or civil rights ideology, and the variance of moral ideology is back to its level of the 1980s. Further, if the depolarization and dealigning trend continues, the moral dimension will have the potential to buffer the disagreement on the other dimensions rather than reinforcing it. This does not mean that conflict on economic or civil rights issues will be reduced due to changes in moral ideology. Instead, even if the public were to become deeply divided on economic or civil rights issues, it will not be difficult to find citizens of the opposing camps sharing similar moral views. This, in turn, will prevent the public from splitting into two consistently opposing subgroups. Of course, this conclusion depends on whether moral issues will maintain their salience in the future. If the continuation of the trends on the moral dimension—decreasing variance, sorting, and inter-dimension correlation—pushes moral issues out of the political discourse, the integrative function of cross-cutting disagreement (Baldassarri and Gelman 2008; Blau and Schwartz 1984; Coser 1956; Schattschneider 1960) will be necessarily reduced. Moral issues would come up less frequently in public as well as private conversations, so citizens might not realize that there is a set of issues on which they can agree; or even if they do, these commonalities might be taken for granted and regarded as politically irrelevant. If so, moral issues would become obsolete and “displaced” (Schattschneider 1960) by other issues. That said, a critique that moral issues were lacking in salience during the period of analysis would be mistaken. Indeed, if there was a period in which the analyzed moral issues were salient, it would be the period under study. Not only was the narrative of the culture war a product of the 1990s and the early 2000s, but it was argued that “conflict extension” (Layman and Carsey 2002; Layman, Carsey, and Horowitz 2006) rather than “conflict displacement” (Schattschneider 1960; Sundquist 1983) has been characterizing the dynamics of public opinion—that is, that the conflict on economic issues has spread over to civil rights and moral issues rather than one being replaced by others. The findings of the analysis offer an important qualification to these interpretations, at least with respect to the moral dimensions over the past decade. Of course, it might be that new moral issues will emerge in the future, become aligned with the conflict on other dimensions, and reinvigorate the culture war. Whether the moral dimension will continue to cut through the disagreement of other dimensions, reemerge as a polarizer, or lose its political importance remains to be seen. Finally, the peculiar trend on the moral dimension sheds some new lights on how public opinion is formed and changed. It is remarkable that the post-millennial reversal in moral ideology occurred in a period when ideology in Congress became unidimensional and polarized. Indeed, if citizens were cue takers, following their counterparts in Congress as it is usually assumed (Carmines and Stimson 1989; Levendusky 2009a; Zaller 1992), ideology in the public should have become a noise-added mirror image of that in Congress. Yet, while citizens followed Congress on economic and civil rights issues by sorting themselves into the “right” camps, a qualitatively different process seems to have driven moral ideology over the past decade. Utilizing a distributional, and hence aggregate, approach to political disagreement, it is difficult if not impossible to identify the micro-mechanisms responsible for the differential trajectories of the ideological dimensions. Also, in absence of an exogenous source of variation, I will have to leave it to future studies to disentangle which of the three disagreement structures was the driving force behind the reversal. We can only speculate that the aggregate trends on morality point toward a bottom-up process, with citizens leading the trend rather than being led by elites. Notes 1 A natural measure of the correlation between the ideology and partisanship would be the Pearson correlation coefficient (e.g., Baldassarri and Gelman 2008; Fiorina and Levendusky 2006) or the difference in mean ideology between Democrats and Republicans (e.g., Bafumi and Shapiro 2009; Hetherington 2009). Yet, if the most liberal Democrat and the most conservative Republican were to become more extreme over time while all others do not change their ideological position, the mean difference between the partisan groups would surely increase. Also, as long as ideology and partisanship are not already perfectly correlated, the correlation coefficient between partisanship and ideology would increase as well. This change in the ideology, however, corresponds to an increase in polarization, as the variance of the overall distribution would increase. The level of sorting, on the other hand, remains the same, since none of the Democrats has changed his or her place with any of the Republicans. 2 Clearly, symbolic ideology, as the term is defined here, does not exhaust all politically relevant symbolic identifications. For example, people might identify symbolically with social movements, their locality, or other social categories. Early studies in voting behavior (e.g., Campbell et al. 1960; Converse 1964) as well as more recent ones (Mason 2016; Perrin, Roos, and Gauchat 2014) have shown that these identifications are important in how individuals gain meaning from the political world. Further, the identification with the labels “liberal” and “conservative” is in part the result of, or at least influenced by, the identifications with such social categories. Yet, whether to include only the identification with the labels or also the identification with other social categories in the definition of symbolic ideology appears to be a definitional issue. Here, following Ellis and Stimson (2012), we take the narrow approach and confine the term to the identification with the ideological labels. 3 For example, even if the true variance of the latent dimension at time t is larger than that at time t+1, the normalizing procedure would rescale the latent dimension of each year to have the same mean and variance (namely, zero and one). 4 The discrimination parameters that I fix are as follows: I fix the government service and spending scale (VCF0839) for the economic dimension, the aid to blacks/minorities scale (VCF0830) for the civil rights dimension, and the abortion item (VCF0838) for the moral dimension. 5 For example, the kurtosis and the bimodality coefficient, which have been used in the literature, suffer from deficiencies outlined in DeCarlo (1997) and Freeman and Dale (2012). The dip test (Hartigan and Hartigan 1985), on the other hand, tests for multimodality, not bimodality. That is, a significant test statistic does not tell us whether the distribution has two, three, or more modes. More importantly, while quantifying the degree of polarization has its merits, to determine whether there is substantively meaningful polarization, graphical explorations of the whole ideological distribution offers more information than single quantitative measures. 6 All results that are referred to but not presented in the paper are included in online appendix B. 7 While it is tempting to compare the standard deviations across dimensions, this is not possible since the scale of each dimension differs. Hence, only the time trend will be interpreted. 8 Due to the failure of respondents to place the stimuli or themselves on the liberal-conservative scale, the number of observations per year are smaller than those used in the analysis of operational ideology. To the extent that the missing pattern in the data affects the results of the analysis, the bias is likely to be toward more polarization and sorting. This is because respondents who fail to place themselves and other stimuli on the liberal-conservative continuum are in general less informed, and tend to report relatively centrist positions (Zaller 1992). 9 For the sake of clarity, outlying observations are not shown. The substantive conclusion does not change when these observations are included (results presented in online appendix B). 10 Time trends of the dispersion as well as the results for the voting population can be found in online appendix B. 11 Confidence intervals were calculated using bootstrapping with 200 replications. 12 Estimating the overlap on operational ideology with only those respondents who were used in the analysis of symbolic ideology does not change the conclusion that the majority of Democrats and Republicans overlap in their operational ideology (see online appendix B). Appendix Item Classification and Parameter Estimates of Graded Response Model Table A1. Posterior Means of Discrimination ( γk) and Cut Point ( κk,c) Parameters, Graded Response Model Results Dimension  Variable  Disc.Param.  Cut 1  Cut 2  Cut 3  Cut 4  Cut 5  Cut 6  Economic  Federal spending - The homeless  1.346  1.252  3.981  —  —  —  —  Economic  Federal spending - Poor/poor people  1.278  0.354  3.581  —  —  —  —  Economic  Federal spending - Assistance to Blacks  1.191  −1.528  1.939  —  —  —  —  Economic  Less government better OR government do more  1.167  0.707  —  —  —  —  —  Economic  Federal spending - Child care  1.077  0.468  3.224  —  —  —  —  Economic  Federal spending - Welfare programs  1.004  −1.843  0.628  —  —  —  —  Economic  Government services/spending scale  1.000  −2.688  −1.588  −0.371  1.280  2.475  3.724  Economic  Federal spending - food stamps  0.970  −1.857  1.095  —  —  —  —  Economic  Govt too involved in things OR problems require  0.928  0.506  —  —  —  —  —  Economic  Guaranteed jobs and income scale  0.879  −2.486  −1.692  −0.908  0.292  1.316  2.497  Economic  Federal spending - public schools  0.859  1.198  3.706  —  —  —  —  Economic  Govt handle economy OR free market can handle  0.851  1.050  —  —  —  —  —  Economic  Federal spending - AIDS research/fight AIDS  0.773  0.671  2.896  —  —  —  —  Economic  Government health insurance scale  0.703  −1.589  −0.858  −0.170  0.840  1.660  2.604  Economic  Federal spending - Fin aid for college students  0.699  0.115  2.641  —  —  —  —  Economic  Federal spending - Social security  0.644  0.489  3.621  —  —  —  —  Economic  Federal spending - Environment  0.638  0.274  3.070  —  —  —  —  Civil rights  Government ensure fair jobs for Blacks  1.290  0.524  —  —  —  —  —  Civil rights  Blacks gotten less than they deserve  1.146  −3.173  −1.128  0.106  2.028  —  —  Civil rights  Civil rights pushes too fast or not fast enough  1.040  −2.317  1.447  —  —  —  —  Civil rights  Blacks should not have special favors to succeed  1.032  −3.512  −1.878  −0.976  0.857  —  —  Civil rights  Aid to Blacks/minorities scale (self-placement)  1.000  −3.168  −2.422  −1.501  0.127  1.035  2.075  Civil rights  Conditions make it difficult for Blacks to succeed  0.934  −2.099  0.000  0.599  2.083  —  —  Civil rights  Affirmative action in hiring/promotion  0.926  −2.409  −1.692  −0.411  —  —  —  Civil rights  Blacks must try harder to succeed  0.897  −2.745  −1.083  −0.245  1.549  —  —  Civil rights  We have gone too far pushing equal rights  0.890  −1.709  −0.374  0.426  2.183  —  —  Civil rights  Government ensure school integration  0.841  0.003  —  —  —  —  —  Civil rights  Big problem that not everyone has equal chance  0.782  −1.384  0.263  0.964  2.707  —  —  Civil rights  Should worry less about how equal people are  0.776  −1.857  −0.460  0.314  1.932  —  —  Civil rights  US fewer problems if everyone treated equally  0.670  −0.739  0.898  1.715  3.332  —  —  Civil rights  Not big problem if some have more chances  0.589  −1.373  0.099  0.967  2.785  —  —  Civil rights  Society ensure equal opportunity to succeed  0.518  0.550  2.225  2.888  4.173  —  —  Civil rights  How much has the position of Blacks changed  0.508  −1.622  0.717  —  —  —  —  Moral  Should gays/lesbians be able to adopt children  2.706  −0.770  —  —  —  —  —  Moral  Favor/oppose gays in military  1.783  −0.303  1.133  1.655  —  —  —  Moral  Newer lifestyles contribute to society breakdown  1.691  −3.632  −2.141  −1.090  0.924  —  —  Moral  Law against homosexual discrimination  1.589  −0.569  0.763  1.619  —  —  —  Moral  Should be more emphasis on traditional values  1.564  −4.572  −3.028  −1.930  −0.017  —  —  Moral  Tolerance of different moral standards  1.303  −1.619  0.463  1.327  2.802  —  —  Moral  Women equal role scale  1.130  0.110  0.880  1.338  2.422  3.060  3.705  Moral  By law, when should abortion be allowed  1.000  −0.433  0.327  2.195  —  —  —  Moral  Should adjust view of moral behavior to changes  0.987  −2.029  −0.276  0.197  1.309  —  —  Moral  When should school prayer be allowed  0.613  −1.991  0.706  2.365  —  —  —  Dimension  Variable  Disc.Param.  Cut 1  Cut 2  Cut 3  Cut 4  Cut 5  Cut 6  Economic  Federal spending - The homeless  1.346  1.252  3.981  —  —  —  —  Economic  Federal spending - Poor/poor people  1.278  0.354  3.581  —  —  —  —  Economic  Federal spending - Assistance to Blacks  1.191  −1.528  1.939  —  —  —  —  Economic  Less government better OR government do more  1.167  0.707  —  —  —  —  —  Economic  Federal spending - Child care  1.077  0.468  3.224  —  —  —  —  Economic  Federal spending - Welfare programs  1.004  −1.843  0.628  —  —  —  —  Economic  Government services/spending scale  1.000  −2.688  −1.588  −0.371  1.280  2.475  3.724  Economic  Federal spending - food stamps  0.970  −1.857  1.095  —  —  —  —  Economic  Govt too involved in things OR problems require  0.928  0.506  —  —  —  —  —  Economic  Guaranteed jobs and income scale  0.879  −2.486  −1.692  −0.908  0.292  1.316  2.497  Economic  Federal spending - public schools  0.859  1.198  3.706  —  —  —  —  Economic  Govt handle economy OR free market can handle  0.851  1.050  —  —  —  —  —  Economic  Federal spending - AIDS research/fight AIDS  0.773  0.671  2.896  —  —  —  —  Economic  Government health insurance scale  0.703  −1.589  −0.858  −0.170  0.840  1.660  2.604  Economic  Federal spending - Fin aid for college students  0.699  0.115  2.641  —  —  —  —  Economic  Federal spending - Social security  0.644  0.489  3.621  —  —  —  —  Economic  Federal spending - Environment  0.638  0.274  3.070  —  —  —  —  Civil rights  Government ensure fair jobs for Blacks  1.290  0.524  —  —  —  —  —  Civil rights  Blacks gotten less than they deserve  1.146  −3.173  −1.128  0.106  2.028  —  —  Civil rights  Civil rights pushes too fast or not fast enough  1.040  −2.317  1.447  —  —  —  —  Civil rights  Blacks should not have special favors to succeed  1.032  −3.512  −1.878  −0.976  0.857  —  —  Civil rights  Aid to Blacks/minorities scale (self-placement)  1.000  −3.168  −2.422  −1.501  0.127  1.035  2.075  Civil rights  Conditions make it difficult for Blacks to succeed  0.934  −2.099  0.000  0.599  2.083  —  —  Civil rights  Affirmative action in hiring/promotion  0.926  −2.409  −1.692  −0.411  —  —  —  Civil rights  Blacks must try harder to succeed  0.897  −2.745  −1.083  −0.245  1.549  —  —  Civil rights  We have gone too far pushing equal rights  0.890  −1.709  −0.374  0.426  2.183  —  —  Civil rights  Government ensure school integration  0.841  0.003  —  —  —  —  —  Civil rights  Big problem that not everyone has equal chance  0.782  −1.384  0.263  0.964  2.707  —  —  Civil rights  Should worry less about how equal people are  0.776  −1.857  −0.460  0.314  1.932  —  —  Civil rights  US fewer problems if everyone treated equally  0.670  −0.739  0.898  1.715  3.332  —  —  Civil rights  Not big problem if some have more chances  0.589  −1.373  0.099  0.967  2.785  —  —  Civil rights  Society ensure equal opportunity to succeed  0.518  0.550  2.225  2.888  4.173  —  —  Civil rights  How much has the position of Blacks changed  0.508  −1.622  0.717  —  —  —  —  Moral  Should gays/lesbians be able to adopt children  2.706  −0.770  —  —  —  —  —  Moral  Favor/oppose gays in military  1.783  −0.303  1.133  1.655  —  —  —  Moral  Newer lifestyles contribute to society breakdown  1.691  −3.632  −2.141  −1.090  0.924  —  —  Moral  Law against homosexual discrimination  1.589  −0.569  0.763  1.619  —  —  —  Moral  Should be more emphasis on traditional values  1.564  −4.572  −3.028  −1.930  −0.017  —  —  Moral  Tolerance of different moral standards  1.303  −1.619  0.463  1.327  2.802  —  —  Moral  Women equal role scale  1.130  0.110  0.880  1.338  2.422  3.060  3.705  Moral  By law, when should abortion be allowed  1.000  −0.433  0.327  2.195  —  —  —  Moral  Should adjust view of moral behavior to changes  0.987  −2.029  −0.276  0.197  1.309  —  —  Moral  When should school prayer be allowed  0.613  −1.991  0.706  2.365  —  —  —  Year  1986  1988  1990  1992  1994  1996  1998  2000  2004  2008  2012  Obs.  2175  2034  1974  2483  1786  1714  1281  1807  1211  2321  2054  Year  1986  1988  1990  1992  1994  1996  1998  2000  2004  2008  2012  Obs.  2175  2034  1974  2483  1786  1714  1281  1807  1211  2321  2054  Note: a) The last two rows show the number of respondents that were used in the scaling procedure. b) None of the 95 percent highest posterior density intervals of the discrimination parameters include zero. Table A1. Posterior Means of Discrimination ( γk) and Cut Point ( κk,c) Parameters, Graded Response Model Results Dimension  Variable  Disc.Param.  Cut 1  Cut 2  Cut 3  Cut 4  Cut 5  Cut 6  Economic  Federal spending - The homeless  1.346  1.252  3.981  —  —  —  —  Economic  Federal spending - Poor/poor people  1.278  0.354  3.581  —  —  —  —  Economic  Federal spending - Assistance to Blacks  1.191  −1.528  1.939  —  —  —  —  Economic  Less government better OR government do more  1.167  0.707  —  —  —  —  —  Economic  Federal spending - Child care  1.077  0.468  3.224  —  —  —  —  Economic  Federal spending - Welfare programs  1.004  −1.843  0.628  —  —  —  —  Economic  Government services/spending scale  1.000  −2.688  −1.588  −0.371  1.280  2.475  3.724  Economic  Federal spending - food stamps  0.970  −1.857  1.095  —  —  —  —  Economic  Govt too involved in things OR problems require  0.928  0.506  —  —  —  —  —  Economic  Guaranteed jobs and income scale  0.879  −2.486  −1.692  −0.908  0.292  1.316  2.497  Economic  Federal spending - public schools  0.859  1.198  3.706  —  —  —  —  Economic  Govt handle economy OR free market can handle  0.851  1.050  —  —  —  —  —  Economic  Federal spending - AIDS research/fight AIDS  0.773  0.671  2.896  —  —  —  —  Economic  Government health insurance scale  0.703  −1.589  −0.858  −0.170  0.840  1.660  2.604  Economic  Federal spending - Fin aid for college students  0.699  0.115  2.641  —  —  —  —  Economic  Federal spending - Social security  0.644  0.489  3.621  —  —  —  —  Economic  Federal spending - Environment  0.638  0.274  3.070  —  —  —  —  Civil rights  Government ensure fair jobs for Blacks  1.290  0.524  —  —  —  —  —  Civil rights  Blacks gotten less than they deserve  1.146  −3.173  −1.128  0.106  2.028  —  —  Civil rights  Civil rights pushes too fast or not fast enough  1.040  −2.317  1.447  —  —  —  —  Civil rights  Blacks should not have special favors to succeed  1.032  −3.512  −1.878  −0.976  0.857  —  —  Civil rights  Aid to Blacks/minorities scale (self-placement)  1.000  −3.168  −2.422  −1.501  0.127  1.035  2.075  Civil rights  Conditions make it difficult for Blacks to succeed  0.934  −2.099  0.000  0.599  2.083  —  —  Civil rights  Affirmative action in hiring/promotion  0.926  −2.409  −1.692  −0.411  —  —  —  Civil rights  Blacks must try harder to succeed  0.897  −2.745  −1.083  −0.245  1.549  —  —  Civil rights  We have gone too far pushing equal rights  0.890  −1.709  −0.374  0.426  2.183  —  —  Civil rights  Government ensure school integration  0.841  0.003  —  —  —  —  —  Civil rights  Big problem that not everyone has equal chance  0.782  −1.384  0.263  0.964  2.707  —  —  Civil rights  Should worry less about how equal people are  0.776  −1.857  −0.460  0.314  1.932  —  —  Civil rights  US fewer problems if everyone treated equally  0.670  −0.739  0.898  1.715  3.332  —  —  Civil rights  Not big problem if some have more chances  0.589  −1.373  0.099  0.967  2.785  —  —  Civil rights  Society ensure equal opportunity to succeed  0.518  0.550  2.225  2.888  4.173  —  —  Civil rights  How much has the position of Blacks changed  0.508  −1.622  0.717  —  —  —  —  Moral  Should gays/lesbians be able to adopt children  2.706  −0.770  —  —  —  —  —  Moral  Favor/oppose gays in military  1.783  −0.303  1.133  1.655  —  —  —  Moral  Newer lifestyles contribute to society breakdown  1.691  −3.632  −2.141  −1.090  0.924  —  —  Moral  Law against homosexual discrimination  1.589  −0.569  0.763  1.619  —  —  —  Moral  Should be more emphasis on traditional values  1.564  −4.572  −3.028  −1.930  −0.017  —  —  Moral  Tolerance of different moral standards  1.303  −1.619  0.463  1.327  2.802  —  —  Moral  Women equal role scale  1.130  0.110  0.880  1.338  2.422  3.060  3.705  Moral  By law, when should abortion be allowed  1.000  −0.433  0.327  2.195  —  —  —  Moral  Should adjust view of moral behavior to changes  0.987  −2.029  −0.276  0.197  1.309  —  —  Moral  When should school prayer be allowed  0.613  −1.991  0.706  2.365  —  —  —  Dimension  Variable  Disc.Param.  Cut 1  Cut 2  Cut 3  Cut 4  Cut 5  Cut 6  Economic  Federal spending - The homeless  1.346  1.252  3.981  —  —  —  —  Economic  Federal spending - Poor/poor people  1.278  0.354  3.581  —  —  —  —  Economic  Federal spending - Assistance to Blacks  1.191  −1.528  1.939  —  —  —  —  Economic  Less government better OR government do more  1.167  0.707  —  —  —  —  —  Economic  Federal spending - Child care  1.077  0.468  3.224  —  —  —  —  Economic  Federal spending - Welfare programs  1.004  −1.843  0.628  —  —  —  —  Economic  Government services/spending scale  1.000  −2.688  −1.588  −0.371  1.280  2.475  3.724  Economic  Federal spending - food stamps  0.970  −1.857  1.095  —  —  —  —  Economic  Govt too involved in things OR problems require  0.928  0.506  —  —  —  —  —  Economic  Guaranteed jobs and income scale  0.879  −2.486  −1.692  −0.908  0.292  1.316  2.497  Economic  Federal spending - public schools  0.859  1.198  3.706  —  —  —  —  Economic  Govt handle economy OR free market can handle  0.851  1.050  —  —  —  —  —  Economic  Federal spending - AIDS research/fight AIDS  0.773  0.671  2.896  —  —  —  —  Economic  Government health insurance scale  0.703  −1.589  −0.858  −0.170  0.840  1.660  2.604  Economic  Federal spending - Fin aid for college students  0.699  0.115  2.641  —  —  —  —  Economic  Federal spending - Social security  0.644  0.489  3.621  —  —  —  —  Economic  Federal spending - Environment  0.638  0.274  3.070  —  —  —  —  Civil rights  Government ensure fair jobs for Blacks  1.290  0.524  —  —  —  —  —  Civil rights  Blacks gotten less than they deserve  1.146  −3.173  −1.128  0.106  2.028  —  —  Civil rights  Civil rights pushes too fast or not fast enough  1.040  −2.317  1.447  —  —  —  —  Civil rights  Blacks should not have special favors to succeed  1.032  −3.512  −1.878  −0.976  0.857  —  —  Civil rights  Aid to Blacks/minorities scale (self-placement)  1.000  −3.168  −2.422  −1.501  0.127  1.035  2.075  Civil rights  Conditions make it difficult for Blacks to succeed  0.934  −2.099  0.000  0.599  2.083  —  —  Civil rights  Affirmative action in hiring/promotion  0.926  −2.409  −1.692  −0.411  —  —  —  Civil rights  Blacks must try harder to succeed  0.897  −2.745  −1.083  −0.245  1.549  —  —  Civil rights  We have gone too far pushing equal rights  0.890  −1.709  −0.374  0.426  2.183  —  —  Civil rights  Government ensure school integration  0.841  0.003  —  —  —  —  —  Civil rights  Big problem that not everyone has equal chance  0.782  −1.384  0.263  0.964  2.707  —  —  Civil rights  Should worry less about how equal people are  0.776  −1.857  −0.460  0.314  1.932  —  —  Civil rights  US fewer problems if everyone treated equally  0.670  −0.739  0.898  1.715  3.332  —  —  Civil rights  Not big problem if some have more chances  0.589  −1.373  0.099  0.967  2.785  —  —  Civil rights  Society ensure equal opportunity to succeed  0.518  0.550  2.225  2.888  4.173  —  —  Civil rights  How much has the position of Blacks changed  0.508  −1.622  0.717  —  —  —  —  Moral  Should gays/lesbians be able to adopt children  2.706  −0.770  —  —  —  —  —  Moral  Favor/oppose gays in military  1.783  −0.303  1.133  1.655  —  —  —  Moral  Newer lifestyles contribute to society breakdown  1.691  −3.632  −2.141  −1.090  0.924  —  —  Moral  Law against homosexual discrimination  1.589  −0.569  0.763  1.619  —  —  —  Moral  Should be more emphasis on traditional values  1.564  −4.572  −3.028  −1.930  −0.017  —  —  Moral  Tolerance of different moral standards  1.303  −1.619  0.463  1.327  2.802  —  —  Moral  Women equal role scale  1.130  0.110  0.880  1.338  2.422  3.060  3.705  Moral  By law, when should abortion be allowed  1.000  −0.433  0.327  2.195  —  —  —  Moral  Should adjust view of moral behavior to changes  0.987  −2.029  −0.276  0.197  1.309  —  —  Moral  When should school prayer be allowed  0.613  −1.991  0.706  2.365  —  —  —  Year  1986  1988  1990  1992  1994  1996  1998  2000  2004  2008  2012  Obs.  2175  2034  1974  2483  1786  1714  1281  1807  1211  2321  2054  Year  1986  1988  1990  1992  1994  1996  1998  2000  2004  2008  2012  Obs.  2175  2034  1974  2483  1786  1714  1281  1807  1211  2321  2054  Note: a) The last two rows show the number of respondents that were used in the scaling procedure. b) None of the 95 percent highest posterior density intervals of the discrimination parameters include zero. 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Social ForcesOxford University Press

Published: Dec 28, 2017

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