Resolution of apparent paradoxes in the race-specific frequency of use-of-force by police

Resolution of apparent paradoxes in the race-specific frequency of use-of-force by police ARTICLE DOI: 10.1057/s41599-018-0110-z OPEN Resolution of apparent paradoxes in the race- specific frequency of use-of-force by police 1 2 1 Cody T. Ross , Bruce Winterhalder & Richard McElreath ABSTRACT Analyses of racial disparities in police use-of-force against unarmed individuals are central to public policy interventions; however, recent studies have come to apparently paradoxical findings concerning the existence and form of such disparities. Although anti- black racial disparities in U.S. police shootings have been consistently documented at the population level, new work has suggested that racial disparities in encounter-conditional use of lethal force by police are reversed relative to expectations, with police being more likely to: (1) shoot white relative to black individuals, and (2) use non-lethal as opposed to lethal force on black relative to white individuals. Encounter- and use-of-force-conditional results, how- ever, can be misleading if the rates with which police encounter and use non-lethal force vary across officers and depend on suspect race. We find that all currently described empirical patterns in the structuring of police use-of-force—including the “reversed” racial disparities in encounter-conditional use of lethal force—are explainable under a generative model in which there are consistent and systemic biases against black individuals. If even a small subset of police more frequently encounter and use non-lethal force against black individuals than white individuals, then analyses of pooled encounter-conditional data can fail to correctly detect racial disparities in the use of lethal force. In more technical terms, statistical assessments of racial disparities conditioned on problematic intermediate variables, such as encounters, which might themselves be a causal outcome of racial bias, can produce mis- leading inferences. Population-level measures of use-of-force by police are more robust indicators of the overall severity of racial disparities than encounter-conditional measures— since the later neglect the differential morbidity and mortality arising from differential encounter rates. As such, population-level measures should be used when evaluating the local-level public health implications of racial disparities in police use-of-force. Research on encounter-conditional use-of-force by police can also fruitfully contribute to public policy discussions, since population-level measures alone cannot address whether racial disparities are driven by disparities in encounters or disparities in use-of-force conditional on encoun- ters. Tests for racial biases in the encounter-conditional use of lethal force, however, must account for individual-level variation across officers in terms of race-specific encounter rates or risk falling to Simpson’s paradox. 1 2 Department of Human Behavior, Ecology and Culture. Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany. Department of Anthropology, University of California, Davis, USA. Correspondence and requests for materials should be addressed to C.T.R. (email: cody_ross@eva.mpg.de) PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 1 | | | 1234567890():,; ARTICLE PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z Introduction Table 1 Population-level police shooting data (as wo recent publications on anti-black, racial disparities in proportions by race/ethnicity) from Ross (2015) and Fryer police shootings in the United States—Ross (2015) and (2016, p. 14) TFryer (2016)—have received media attention (e.g., Cox, 2016; Li, 2016; DeVega, 2016), in part because they appear to Source Armed status Black Hispanic White reach opposite conclusions concerning police behavior. Ross US Census – 0.13 0.29 0.58 (2015) shows that at the population-level individuals are about 3.5 (2010) times more likely to be black, unarmed, and shot-by-police, than Fryer (2016) All shootings 0.46 0.30 0.24 white, unarmed, and shot-by-police, adjusting for relative dif- Ross (2015) All shootings 0.38 0.38 0.24 ferences in population size. Fryer (2016), however, finds that Ross (2015) Unarmed 0.36 0.38 0.26 conditional on being encountered by police, black civilians relative individuals to white civilians are less likely to be shot by police. Such To increase comparability to the Fryer (2016) study, census data and the police shootings data apparently conflicting results have generated confusion in the from Ross (2015) have been taken only from counties where Fryer (2016) also had data. These public presentation of these two studies. The key difference counties are: Dallas, TX; Harris, TX; Travis, TX; Suffolk, MA; Camden, NJ; Pinellas, FL; Lee, FL; Orange, FL; Palm Beach, FL; Duval, FL; Brevard, FL; and Los Angeles, CA. The population data between them, however, is that Ross (2015) looks at population- show that in these counties, about 13% of residents are black, 29% of residents are of Hispanic level relative risk, whereas Fryer (2016) looks at relative risk origin, and 58% of residents are white. When considering the proportion of police shooting victims by race, the data from Fryer (2016) and Ross (2015) are very similar; both studies find conditional on encounters or use-of-force. These studies thus tell that black individuals are killed by police in greater proportions than would be expected given us different things; failure to detect racial disparities in police their race-specific population levels shootings conditional on encounters does not imply absence of racial disparities in police shootings at the population level. Even conditional rates of the use of lethal force by police may arise in light of the well-acknowledged shortcomings in the data used not from bias against white individuals, but rather from elevated in each of these studies, each exposes complementary elements of rates of unjustifiable encounters with black individuals. In order a coherent picture of the dynamics of police use-of-force. to disentangle which of these possibilities best explains the In order to gain a more fine-grained understanding of why the empirical data, future research will need to better account for encounter-conditional results of Fryer (2016) seem to run so variation across officers in terms of: (1) their race-specific, contrary to what might be expected given the population-level exposure-time conditional encounter rates with civilians, (2) their findings of Ross (2015), we derive a generative model of police race-specific, exposure-time conditional rates of use-of-force, and use-of-force outcomes, and then analyze the conditions under (3) their race-specific probabilities of use-of-force conditional on which this model can generate data consistent with both analyses. encounter. We use both analytic and simulation methods to draw attention to some counter-intuitive properties of this model. Specifically, we draw a parallel to classic findings on Simpson’s Paradox in Population-level analyses. In Table 1 we present comparable, applied statistics (Simpson, 1951; Bickel et al., 1975; Pearl, 2014), population-level data from Ross (2015) and Fryer (2016); the and demonstrate that pooled analyses of encounter-conditional outcomes are very similar. Both studies find that black individuals data—as in Fryer (2016)—will fail to find true encounter- are killed by police in greater proportions than would be expected conditional anti-black racial disparities over a wide range of given their relative population size. In fact, the data mobilized by parameter values when there is heterogeneity in the rates with Fryer (2016) show greater evidence of racial disparities in police 46% = 3.5x, than do the data which police encounter and use non-lethal force as a function of shootings at the population level: 13% 38% suspect race. For example, if even a small subset of police have presented by Ross (2015) in comparable counties: = 2.9x. See 13% propensities to more frequently encounter black relative to white also a similar comparison including data from The Guardian, The individuals, then analyses of pooled encounter-conditional data Washington Post, and VICE (Fryer, 2017). Hispanic individuals will fail to detect systemic anti-black racial disparities in the are shot in direct proportion to their population levels in the data 30% encounter-conditional use of lethal force by the larger subset of provided by Fryer (2016): = 1.0x, and at rates slightly above 30% 38% police. Likewise, if even a small subset of police are more likely to their population levels in the data provided by Ross (2015): = 30% non-lethally assault black individuals than white individuals— 1.3x. Finally, both studies agree numerically that white indivi- e.g., with tasers—in contexts when such force is not actually duals are shot at a rate less than that which would be expected 24% justified, and then report that such force was justified, analyses of given their population levels: = 0.4x, despite the fact the 58% pooled use-of-force-conditional data will suggest that lethal force authors use different data collection methodologies over different is more likely to be used against white relative to black time intervals. As such, the analyses of Ross (2015) and Fryer individuals. (2016) are in general agreement concerning the existence and In the analysis that follows, we demonstrate three important magnitude of population-level racial disparities in police conclusions: (1) Ross (2015) and Fryer (2016) document quan- shootings. titatively similar population-level anti-black racial disparities in The Ross (2015) analysis is resolved to the level of county, and the use of lethal force by police, (2) analyses of encounter- shows significant geographical diversity in the levels of racial conditional rates of the use of lethal and non-lethal force by disparities in police shootings—variation that has the potential to police are insufficient to address predictions about racial dis- advance explanations of the locally contextualized causes of police parities in policing, since they neglect the relative risk of being shootings and to identify the locales that may benefit most from encountered by police in the production equation of population- policy review. However, Ross (2015) has no data on race-specific level racial disparities; and, most critically, (3) the findings of encounter rates between police and civilians and therefore cannot Fryer (2016) suggesting null or anti-white disparities in the address the race-specific probabilities of being shot by police encounter-conditional rates of the use of lethal force by police are conditional on being encountered by police. Fryer (2016), by actually consistent with a situation in which all police have ele- contrast, has compiled a much more detailed dataset for a more vated encounter-conditional rates of the use of lethal force against limited sample of places and departments; as such, the data black individuals, but a small subset of police encounter and provided by Fryer (2016) allow for a more thorough micro-level assault black individuals sub-lethally at elevated rates. In other analysis of the generative pathways of racial disparities in police words, apparent anti-white racial disparities in encounter- use-of-force in specific locations. 2 PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms | | | PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z ARTICLE The data in Ross (2015) could be biased by selective reporting, Ross (2015) and the encounter-contingent results of Fryer (2016), for instance were individual engaged in the crowd-sourcing effort including: to have preferentially reported police shootings of unarmed black 1. Elevated population-level rates of police encounters with civilians, rather than following the random sampling methodol- black individuals relative to white individuals—see Fryer ogy procedure requested by Wagner (2014). Likewise, the data in (2016, Table 1A, Panel A) and Fryer (2016, Table 1D, Panel Fryer (2016) could come from a biased sample of departments. A). Nevertheless, both studies show remarkably similar findings when 2. Elevated population-level rates of lethal force against black comparable, population-level measures are used. This initial individuals relative to white individuals—see Ross (2015) and comparison serves to cross-validate, to some extent, both data Fryer (2016, Table 1C, Panel A). sources for studying population-level disparities in police use-of- 3. Elevated encounter-conditional rates of non-lethal force force. against black individuals relative to white individuals—see Fryer (2016, Table 2A) and Fryer (2016, Table 2B). And the so-called paradoxes in otherwise consistent Encounter-conditional analyses. Given the general agreement of patterns: the population-level results between these two studies, at first 4. Elevated encounter-conditional rates of lethal force against pass the encounter-conditional results of Fryer (2016)are white individuals relative to black individuals—see Fryer striking. Drawing on his micro-level data, Fryer (2016) finds (2016, Table 5). consistent, strong, and significant levels of anti-black racial dis- 5. Elevated probability ratios of the use of non-lethal force to parities in police use of non-lethal force in graded categories lethal force against black individuals relative to the same ratio from hands on, to handcuffing, display of a weapon, use of against white individuals—see Fryer (2016, Table 5). pepper spray, and use of a baton. These racial disparities remain unexplained even after accounting for 112 (Fryer, 2016,p. 17) context-dependent covariates. But, in a result he describes as a Informal model description. Informally, the model we use “stark contrast to non-lethal uses of force” (p. 5), he finds that entails a homogeneous police force, and sub-populations of black use of lethal force by police actually shows reversed, anti-white, and white citizens. The model makes explicit assumptions about racial disparities; black individuals are less likely than white police behavior concerning race-specific rates of police encoun- individuals to be shot by police, conditional on being encoun- ters with citizens, and the probabilities of the use of no force, tered by police. non-lethal force, or lethal force by police conditional upon This result has been emphasized in media accounts and is encounter. The model provides a demonstration of the manner in surprising in light of general findings on racial disparities in which an apparently paradoxical result (the simultaneous truth of police use of both lethal and non-lethal force spanning several all five of the observations listed above) is fully consistent with decades and literatures—i.e., research on implicit psychological police use-of-force being systematically biased against black biases (Plant et al., 2005; Correll et al., 2006, 2007), sociological individuals. drivers of racial disparities (Jacobs, 1998; Smith, 2003; Bergesen, 1982; Gilbert and Ray, 2016), structural disparities established by Formal model description. Formally, our model assumes that we the existing social order (Harring et al., 1977; Jacobs and Britt, have a population of N individuals, with black and white sub- 1979; Holmes, 2000), proximate responses by police to areas of populations N and N , where: N = N + N . Note that we will B W B W high crime and risk (Jacobs, 1998; Fyfe, 1980), racial bias in continue to use subscripts of B and W to refer to black and white profiling and encountering individuals (Warren et al., 2006; sub-populations, and that all parameters are defined in Table 2 Tomaskovic–Devey et al., 2004; Gelman et al., 2007), blatant for ease of reference. We assume that over some interval of time, racism (Goldkamp, 1976; Martinot and Sexton, 2003; Doane, E and E individuals are encountered by police, at rates: ϕ ∈ [0, B W B 2006), and social dominance orientation (Sidanius and Pratto, 1] and ϕ ∈ [0, 1]. As such, we expect the counts of encounters to 2001), over many geographic areas: United States (Ross, 2015; follow: Hirschfield, 2015), Canada (Wortley and Tanner, 2003; Wortley E  Binomial N ; ϕ ð1Þ and Owusu–Bempah, 2012), Brazil (Cano, 2010; French, 2013), B B B and South Africa (Brogden and Shearing, 2005). Nonetheless, the widely publicized interpretation of Fryer (2016)—one that he E  Binomial N ; ϕ ð2Þ W W W himself highlights—is that police do not show anti-black racial bias in the use of lethal force. While we do not doubt that this pattern is apparent in the analyzed data, we take issue with We then assume that conditional upon encountering a civilian, interpretation, given that other aspects of Fryer’s analysis suggest police engage in the use of either no force, non-lethal force, or that Simpson’s paradox could be driving this effect (Simpson, lethal force. Let the parameters: θ ∈ [0, 1] and θ ∈ [0, 1] define B W 1951; Pearl, 2014; Bickel et al., 1975, and see Discussion). In the the probability of the use of lethal force conditional upon following sections, we show that the encounter-contingent results encounter, and the parameters: γ ∈ [0, 1−θ ] and γ ∈ [0, 1 B B W of Fryer (2016) are consistent—perhaps counter-intuitively so— −θ ]define the probability of the use of non-lethal force with systemic and consistent anti-black racial disparities in police conditional upon encounter. The probability of police using no encounter rates and in the subsequent rates of the use of both force on white and black individuals upon encounter is then given lethal and non-lethal force upon encounter. by: 1−(θ + γ ) and 1−(θ + γ ), respectively. W W B B Then, to define the counts of lethal force by police, S and S , B W and non-lethal force by police, G and G , we write: B W A generative model of racial disparities in use-of-force by ðS ; G ; O Þ′  Multinomial E ; ðθ ; γ ; 1 ðθ þ γ ÞÞ′ ð3Þ police B B B B B B B B We resolve the counter-intuitive results by using a generative model to demonstrate that increased racial disparity in the rates ðS ; G ; O Þ′  Multinomial E ; ðθ ; γ ; 1 ðθ þ γ ÞÞ′ W W W W W W W W at which a subset of police engage civilians with non-lethal force ð4Þ will generate all patterns found in the population-level results of PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 3 | | | ARTICLE PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z Table 2 Model variables and relationships. Subscripts B and W refer to black and white sub-populations, respectively Variable Definition Formula(s) Domain N Population under consideration N= N + N 2 N W B E Count of individuals subjected to a police encounter Eqs. (1) and (2), text ∈{1, …, N} S Count of lethal police actions Eqs. (3) and (4), text ∈{1, …, E} G Count of non-lethal police actions Eqs. (3) and (4), text ∈{1, …, E} ϕ Probability of encounter with police ∈[0, 1] θ Probability of receiving lethal force, conditional on encounter ∈[0, 1] γ Probability of receiving non-lethal force, conditional on encounter ∈[0, 1 − θ] ψ Population-level rate of lethal police actions ψ= ∈[0, 1] δ Population-level rate of non-lethal police actions δ = ∈[0, 1] Φ Relative population-level risk of being subjected to a police encounter Φ = ∈[0, ∞) Θ Relative risk of being the victim of a lethal police action conditional upon encounter Θ = ∈[0, ∞) Γ Relative risk by being of being the victim of a non-lethal police action conditional upon Γ= ∈[0, ∞) encounter Ψ Relative population-level risk of being the victim of a lethal police action Ψ = ∈[0, ∞) Δ Relative population-level risk of being the victim of a non-lethal police action Δ = ∈[0, ∞) The “hat” symbol used in the text indicates parameter values unique to the routine over-escalation sub-model; the parameters without the “hat” symbol refer to the standard policing model. We note that the term “non-lethal” includes sub-lethal violent engagements, but excludes non-violent engagements Table 3 Conditions for the presence or absence of racial disparities and their direction if present Form of bias Absent Present Against black individuals Against white individuals Encounter ϕ = ϕ ⇔ Φ = 1 ϕ > ϕ ⇔ Φ >1 ϕ < ϕ ⇔ Φ <1 B W B W B W Population-level, non-lethal force δ = δ ⇔ Δ = 1 δ > δ ⇔ Δ >1 δB < δ ⇔ Δ <1 B W B W W Population-level, lethal force ψ = ψ ⇔ Ψ = 1 ψ > ψ ⇔ Ψ >1 ψ < ψ ⇔ Ψ <1 B W B W B W Encounter-conditional, non-lethal force γ = γ ⇔ Γ= 1 γ > γ ⇔ Γ >1 γ < γ ⇔ Γ <1 B W B W B W Encounter-conditional, lethal force θ = θ ⇔ Θ = 1 θ > θ ⇔ Θ >1 θ < θ ⇔ Θ <1 B W B W B W Variables are defined in Table 2; the double arrow (⇔) is read as “is equivalent to” where: O = E −(S + G ) and O = E −(S + G ), meaning and encounter-conditional use of non-lethal and lethal force (see B B B B W W W W that the outcome vectors contain the predicted counts of lethal Table 3). force, non-lethal force, and no force, given the number of For example, we would consider disparity in encounters to be encounters and the probability parameters for each use-of-force absent if race-specific rates of encounters are equal: ϕ = ϕ . This B W category. is the same as saying that the relative risk of encounter by race is Finally, we can write the total population-level rates of the use equal to one: Φ = 1, or that the log of this value is equal to zero: S S of lethal force as: ψ = B= and ψ = W= , and the total log(Φ) = 0. We would consider encounters to be structured N N B W B W population-level rates of non-lethal force as: δ = = and δ = against black individuals if: ϕ > ϕ , or equivalently if: Φ >1, or B N W B W W= . The population-level relative risk of being the victim of a finally, if: log(Φ) > 0. Reversing the inequalities would indicate lethal police action, Ψ, is then given as: Ψ = B= . The disparities against white individuals. The remaining four types of population-level relative risk of being the victim of a violent disparities are described in the same fashion. but non-lethal police action, Δ, is given as: Δ = B= . The relative risk of being encountered by police, Φ,isdefined as: Φ = B= . The standard policing model. We name the full generative The relative risk of being the victim of a lethal police action model described above the standard policing model, and take it to conditional on being encountered by police, Θ, is given as: Θ = define the universe of standard police interactions, although there B= . The relative risk of being the victim of a violent but non- W may be either unjustifiable (implicit or explicit bias) or justifiable lethal police action conditional on being encountered by police, Γ, (a response to crime) racial disparities in the rates of encounters is given as: Γ = B= . W or use-of-force in this model. At this point, we note a key dependency in the model. The overall counts of lethal and non-lethal force depend on the rates Assessing sources of disparities.Wedefine racial disparities as of encounters given by ϕ and ϕ , via the counts E and E . This W B W B the disproportionate representation of a racial sub-group in a gives us our first insight on the apparent paradox that population- particular type of police action category. That is, we seek here to level analyses of U.S. data show anti-black racial disparities in avoid any prejudicial connotations of the term, as we do not police shootings, while encounter-contingent analyses show know, or need to know for the narrow purposes of our analysis, if reversed, anti-white disparities. A difference in race-specific such disparities are justifiable in some manner or not. We encounter rates could lead to population-level racial disparities in recognize five ways in which racial disparities may occur or be police shootings, even in the absence of racial disparities in police documented as absent: in encounters, and in the population-level shootings conditional on encounter. 4 PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms | | | PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z ARTICLE ^ ^ More formally, the log of the expected population-level extent parameters: ϕ 2½0; 1 and ϕ 2½0; 1. As such, we expect the B W of racial disparities in police shootings is approximately: counts of these encounters to follow: _ ð6Þ E  BinomialðN ; ϕ Þ logðE½ΨÞ  logðΘÞþ logðΦÞð5Þ B B B for N sufficiently large and θ ϕ not too small (see ^ ^ ð7Þ W W W E  BinomialðN ; ϕ Þ W W Supplementary Materials for derivation). Even if police are more likely to use lethal force against white people than black people The counts of lethal and non-lethal force events resulting from conditional on encounter (i.e., log(Θ) < 0, which might be these interactions are then given by: expected if police preferentially encounter white individuals ^ ^ ^ ^ ^ ^ ðS ; G ; O Þ′  MultinomialðE ; ðθ ;^γ ; 1 ðθ þ ^γ ÞÞ′Þ ð8Þ B B B B B B B B engaging in crimes, but encounter black individuals more frequently or haphazardly), then we will still see population- level anti-black racial disparities in police shootings on average so ^ ^ ^ ^ ^ ^ ðS ; G ; O Þ′  MultinomialðE ; ðθ ;^γ ; 1 ðθ þ ^γ ÞÞ′Þ W W W W W W W W long as the relative risk of encounters (i.e., log(Φ)) is large enough ð9Þ to compensate. This might also occur if the threshold of suspicion leading to an encounter is lower for black individuals than for ^ ^ ^ ^ ^ ^ ^ ^ where O ¼ E ðS þ G Þ and O ¼ E ðS þ G Þ. Equa- B B B B W W W W white individuals. Note also that the final population-level metric tions (6), (7), (8), and (9) are of the same form as Eqs. (1), (2), (3), is the more appropriate indicator of the public health issue at and (4) in the standard policing model. The parameters also are hand; regardless of whether differential rates of encounters or the same in definition, with the “hat” symbol indicating that they differential use-of-force conditional on encounters drives differ- refer to the routine over-escalation model and can take on ential morbidity and mortality rates, the end result is the same— different values than in the standard policing model. The logical greater overall morbidity and mortality from police per unit conditions establishing the presence or absence of racial population. This being said, the results of Fryer (2016)—should disparities in this model are the same as those given in Table 3. they replicate under individual-level analyses that control for the If the population of officers is composed of some police possible dynamics discussed in this paper—provide the key operating under the standard parameters, and some operating insight that reduction in population-level racial disparities in under the routine over-escalation parameters, then the joint police use-of-force might depend more on attenuation of racial mixture model is able to produce the aggregate appearance of disparities in encounter rates than on changes in how officers anti-white disparities in lethal force conditional on encounter respond to suspects conditional on their race. ^ ^ S þS S þS B B W W (i.e., < ), even when there are no anti-white racial ^ ^ E þE E þE B B W W The routine over-escalation model. The above result suggests disparities in the use of lethal force conditional on encounter in ^ ^ that sub-structure in the behavioral patterns of police which S S S S B W B W either subgroup of police (i.e., > and > ). The easiest ^ ^ E E B W E E increases their rate of non-lethal encounters with black indivi- B W S S B W sufficient condition to understand arises when set ¼ λ, with duals will have the effect of diminishing the apparent rate of lethal E E B W outcomes conditional on encounters, while leaving the λ > 1, and then make the assumption that the count of lethal force population-level rates of racial disparities in police shootings incidents against white individuals in the routine over-escalation unchanged. To formally explore this idea, we introduce a second sub-model declines to zero (i.e., S ! 0). Even under these generative model below. conditions, we show (in the Supplementary Materials) that this Assume that there is heterogeneity in the types of encounters model produces an apparent absence of encounter-conditional with police—e.g., i) those resulting from police operating under anti-black racial disparities—actually anti-white racial disparities standard protocols and ii) those resulting from police engaging in —in the use of lethal force whenever: more routine and excessive use of non-lethal force. If this is the E E B W case, then the probability that white individuals will be more λ < ð10Þ ^ ^ likely than black individuals to receive lethal force conditional on ðE þ E Þ ðE þ E Þ B B W W encounter grows as the small subset of police that engage in excessive use of non-lethal force target black people at increasing This expression indicates that as long as there are sufficient rates. This effect holds even when all parameter values (i.e., anti-black racial disparities in the frequency of encounters arising encounter rates, and rates of the use of lethal and non-lethal force from the routine over-escalation model to offset the anti-black conditional on encounter) are structured against black individuals racial disparities in the use of force conditional on encounter in in both subsets of police officers. the standard policing model, we will observe an apparent absence We demonstrate this result by defining an additional sub-model, of anti-black disparities in the use of lethal force conditional on the routine over-escalation model. In this model, some small subset encounter in the pooled data. In the language of the model, if E of police officers are more prone to engage in additional illegitimate is sufficiently large relative to other terms, then it can offset a λ > and unnecessary encounters with individuals. While it is not 1. For example, if the encounter-conditional black to white necessary to provide a reason for why we might see such relative risk of being shot by police were λ = 1.11, then if just 1 in heterogeneity in officer propensities, a body of research in social 20 white encounters, but 3 in 20 black encounters occur under the dominance theory (e.g., Sidanius et al., 1994; Sidanius and Pratto, routine over-escalation model, we would still—perhaps para- 2001) provides some coherent explanations. Since the individuals doxically—see aggregate-level anti-white racial disparities in encountered in these cases are not necessarily encountered on encounter-conditional use of lethal force by police. reasonable suspicion of a crime, we assume that use of lethal force conditional on encounter is less likely than under the standard policing model, butthatuse of non-lethal forceiselevated. Implications of our model for statistical analysis of police We assume that over the same interval of time as in the shooting data. To emphasize the implications of our findings for ^ ^ standard policing model, E and E individuals in each respective empirical analyses, we present in the Supplementary Materials an B W sub-population get encountered by the subset of police who additional analysis in which we simulate data on police encoun- engage in excessive use of non-lethal force, at rates given by the ters under the union of the standard policing and routine over- PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 5 | | | ARTICLE PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z escalation models. We then analyze the aggregate data with a complete reversal in encounter-conditional rates of lethal force. statistical model that ignores the fact that the use-of-force out- Our model results, however, establish that precisely this set of comes arise through a generative model structure with hetero- racial disparities in rates of encounters and use of non-lethal force geneous decision making units (i.e., the above-listed sub-types of can lead to the principle finding of Fryer (2016). police officers). The results again confirm that the “paradoxical” Our findings parallel classic results in applied statistics related results with which we began are only apparent. Furthermore, we to Simpson’s paradox (e.g., Simpson, 1951; Bickel et al., 1975); show that a wide range of parameter values are sufficient to analysis of aggregate data (i.e., data arising from pooling the produce the seemingly paradoxical results and demonstrate that outcomes of heterogeneous decision-making units) can show the phenomenon does not strongly depend on the particular discrimination against a given class of individuals, even when reducing assumptions used to reach an analytical solution. there is actually discrimination in the opposite direction in every decision-making unit. Disparities in the rates with which indivi- duals interact with each decision-making unit are typically found Discussion in cases where Simpson’s paradox is demonstrated. For example, The data and methodological approach presented in Fryer (2016) in the case of the Berkeley graduate admissions data (Bickel et al., represent the most important advance to date in the analysis of 1975), women tended to apply to departments that were more race-specific of use-of-force by police. Fryer (2016) is able to difficult for applicants of either sex to enter, while men tended to investigate aspects of police use-of-force (like encounter-condi- apply to departments that accepted a greater majority of appli- tional, race-specific rates of the use of lethal force) that have thus cants of either sex; as a result, in the aggregate, men were accepted far been opaque. However, this new ground brings with it some in greater proportion than women, despite the fact that there was counter-intuitive terrain for analysts and for the journalists who actually evidence of a small average bias in admitting women at summarize research for the public. Specifically, we show that the the level of the decision-making unit. presentation of Fryer’s results as indicating an absence of anti- The case of racial disparities in police shootings conditional on black racial disparities and perhaps even the presence of anti- encounter holds a similar logical structure. However, the variable white racial disparities in police use of lethal force is unwarranted. that structures decision-making (akin to the academic depart- Both Ross (2015) and Fryer (2016) show population-level anti- ment in the Berkeley graduate admissions data) is much harder to black racial disparities in the use of lethal force by police—dis- empirically identify in the case of police shootings. We show that parities that are indicative of disproportionate morbidity and racial disparities in encounter rates can generate Simpson’s mortality per unit population. The theoretical model presented paradox, and we provide an example of a kind of decision- here allows us to decompose these disparities into the effects of structuring variable (whether a given officer has standard policing differential encounters and differential the use of lethal force or routine over-escalation parameters) which produces model conditional on encounters. Either of these statistical biases may be outcomes that are similar to the empirically observed data. It will justifiable on the basis of differential crime rates or con- likely be difficult to empirically evaluate if Simpson’s paradox textualizing details. The narrow objective of our analysis, how- truly explains the results of Fryer (2016) since the longitudinal, ever, does not require we take a position as to whether or not individual-level data needed to estimate more finely-resolved differential encounters and differential use of force are justified. model parameters will be very hard to acquire. Nonetheless, this Nonetheless, the existence of population-level disparities in police point is largely eclipsed by a more important point—namely, that use-of-force raises social and policy issues that must be addressed. the public health implications of racial disparities in police Taking the analysis of Fryer (2016, 2017) at face value, it would shootings and non-lethal use-of-force (e.g., Miller et al. 2017; appear that race-based differences in the use of lethal force con- DeVylder et al., 2017; Ross, 2017), in the end, come down to the ditional on encounter can be entirely explained by contextualizing population-level relative risk not the encounter-conditional risk. details. But, as we show, if police behavior is heterogeneous, with most officers following standard protocol and a small subset of officers engaging in unwarranted use of excessive non-lethal force Pathways leading to population-level racial disparities in police (like use of tasers), racial disparities in who this subset of officers use-of-force. While the use of lethal force against unarmed target can complicate interpretation of encounter-conditional individuals by police is quite rare, it does occur and with racial data. It is ironic that elevated levels of sub-lethal assault against disparities in population-level rates. Non-lethal force also is dis- innocent black individuals by a subset of police would have the proportionate at the population level (Fryer, 2016; Miller et al., effect of diminishing the apparent severity of anti-black racial 2017). These observations are not contradicted by the observation disparities in lethal force conditional on encounter in the full set of that the encounter-conditional probabilities of lethal outcomes by officers. Nevertheless, this is a key finding of our model. Increased race are reversed in aggregate data. While Fryer (2016) and Ross encounter rates and excessive use of violent but non-lethal force (2015) address somewhat different questions, each using variables by a subset of police against black individuals can mask the unique to their datasets, they arrive at complementary, not existence of anti-black racial disparities in the encounter- paradoxical, conclusions. Those conclusions reinforce the pre- conditional use of lethal force by police in pooled data. vailing consensus that there are significant racial disparities in Given that the existence of racial disparities in police use-of- police behavior at the population level, and together they provide force is a serious public policy issue (e.g., USDOJ, 2016), it is an expanded basis for appreciating that this is a complex problem critical that these dynamics be understood. Although the work of at the local level Fryer (2016), with significant differences among Fryer (2016) presents one of the most detailed empirical analyses locales nationally Ross (2015). of racial disparities in police use-of-force, only individual-level Within each locale, the research strategy advanced by Fryer estimates of officer parameters will allow a convincing demon- (2016)isimportant,asitallows ustomovebeyond simply stration of his arguments. Though it is impossible to demonstrate demonstrating the presence of disparities and instead investigate strictly though our modeling effort here, it seems improbable that how and why such disparities arise when and where they do. there would be such consistent evidence of racial disparities in Without being able to identify the causal drivers of racial disparities rates of: (i) encounters with police, (ii) population-level and operating in a given location we are unable to offer useful policy encounter-conditional use of non-lethal force by police, and (iii) recommendations (Ross, 2016). It is important to determine if racial population-level use of lethal force by police, only to see a disparities in a particular locale arise due to officer behavior 6 PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms | | | PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z ARTICLE conditional on encounter, or via the policies and social contexts the police were obliged to investigate, often after being primed leading to racial disparities in encounter rates. The combination of that the indicated persons posed a threat. explicit theoretical modeling of the generative pathways of use-of- Black Americans are disproportionately likely to be encoun- force outcomes, wariness concerning Simpson’sparadox,and mixed tered by police, be the victims of violent but non-lethal use-of- use of both qualitative and quantitative methods will help force by police, and be the victims of lethal use-of-force by police. researchers better understand the empirical data. However, these observations are fully consistent with the observation that the great majority of individual officers do not Officer behavior. Police officers and police departments are disproportionately target black people based on their own diverse, and it is inappropriate to characterize such institutions in personal discretion and do not show racial bias in the use of monolithic terms. There is no shortage of cases of police officers lethal or non-lethal force conditional on encountering a given engaging in overt racism in recent years (e.g., cases in Los individual. Social context is likely to play a significant role in Angeles, (Stack, 2016; Whaley, 2013), Oakland, CA (Shoichet explaining differential encounter rates and their downstream et al., 2016), San Francisco, CA (Serna and Romney, 2015; Serna, effects on population-level racial disparities in police use-of-force. 2016), San Diego, CA (Perry, 2015), Miami, FL (Buncombe, 2015), Fort Lauderdale, FL (Barszewski, 2016), Clatskanie, OR Social context, policies, and encounter rates. Recent data show that (Park, 2015), Seattle, WA (Campbell, 2015), New York, NY black individuals are more likely to be stopped by police than (Sapien, 2015), Camden, NJ (Walsh, 2016), Edison, NJ (Amaral, white individuals (Fryer, 2016; Miller et al., 2017; USDOJ, 2016). 2015), Ferguson, MO (Swaine, 2014), Saint Louis, MO (Hudson, Miller et al. (2017) argue that the differential population-level 2014), Cleveland, OH (Hensley, 2014), Detroit, MI (Murphy, rates of the use of lethal force by police are almost entirely 2013), New Orleans, LA (McCarthy, 2012), Baton Rouge, LA explainable by these disparities in encounters—an interpretation (Alejandro, 2014), Chicago, IL (Stahl, 2008), Baltimore, MD which is not inconsistent with our present analysis. There are two (USDOJ, 2016), and other locations). Excessive media and public major lines of argument concerning the causes of differential focus on the sensationalized cases mentioned above, however, has encounter rates: (1) that differential encounter rates are driven by the potential to wrongfully impute such attitudes to police officers differential rates of crime, and (2) that the ‘criminalization of in general, trigger in-group out-group identity politics, and to blackness’ leads to racial disparities in encounters for reasons distract from the dialog needed to implement effective policies having little to do with differential crime rates. addressing the problem. While is important to end impunity for In the aggregate in the United States, there appear to be higher the small subset of officers who abuse their positions of power per capita rates of violent crime committed by black individuals and responsibility, or display outward signs of racist hatred like relative to white individuals (e.g., USDOJ, 2014)—the caveat is some of those mentioned above, it is also important to identify that these arrest/conviction records may themselves be an the less visible, institutional drivers of racial disparities in police outcome of racial disparities in policing intensity and conviction use-of-force. rates. But, there is no evidence to suggest that the counties with There is increasing evidence that the population-level presence relatively high black to white crime rate ratios are those with of racial disparities in police shootings might have less to do on disproportionally high rates of racial disparities in police use of average with officer behavior conditional on encounter, and more lethal force against unarmed individuals (Ross 2015); however, to do with differences in encounter rates (Fryer, 2016; Miller the analysis of Ross (2015) linking county-level crime rates and et al., 2017. This information may be key to creating more racial disparities in police shootings is itself very susceptible to the effective policy change. Selby et al. (2016) have compiled a ecological inference fallacy. This being said, other more detailed, detailed data set of officer caused deaths of unarmed individuals geographically localized studies have also found racial disparities in the United States in 2015. At the population level, their data in rates of encounters and use-of-force that are not fully closely echo those of Ross (2015) and Fryer (2016)—black explainable by differential crime rates or related variables (e.g., individuals represent about 42% of the victims of known race, Fryer, 2016; Gelman et al. 2007; USDOJ, 2016). 42% despite being only about 12% of the population ( = 3.5x), Explanations for differential encounter rates based on the 12% while non-Hispanic white individuals represent about 39% of the 'criminalization of blackness' tend to hold strong narrative weight victims of known race, but make up about 62% of the population but are more difficult to confirm with empirical data. The 39% ( = 0.63x). Selby et al. (2016), however, investigate the principle idea is that black individuals are more likely to be 62% contextualizing details of each case, and find that there is no reported by community members to the police than white evidence to suggest that overt or even unconscious racial individuals—especially in socio-economically unequal areas—for prejudice plays a systematic role in the officer-involved deaths innocuous activities like smoking a cigarette at night, jogging, of unarmed citizens—which is not to say that cases to the walking or driving in ‘the wrong kind of neighborhood’, wearing contrary never occur. Instead, their findings point to other hoodie-style sweat shirts, driving nice cars, driving not-so-nice characteristics associated with the victim, including acute drug cars, etc. (Beer, 2016); there is a body of qualitative literature of intoxication, mental and physical illness, violent behavior, and this topic, and arguments linking community behaviors and perceived threats to innocent civilians as being critical predictors biases in the representations of black people by the U.S. media of the deaths of unarmed civilians due to police intervention (see further discussion in the Supplementary Materials). How- (Selby et al. 2016). Further, Selby et al. (2016) and Ross (2015) ever, fine-grained, geographically representative quantitative data both note that most civilians who are shot by police were armed on the disproportionate rates at which black individuals are at the time of the incident. reported to the police for innocuous activities appear to be Additionally, Selby et al. (2016) mention that in about 88% of unavailable. Production of this kind of data would be a fruitful the lethal police encounters not beginning with traffic stops, direction for future research. officers engage suspects only after being requested to do so by the Other dynamics might lead to disproportionately high rates of community (i.e., via 911 calls). As such, these encounters are not encounters between black individuals and police. Racial dispa- initiated at the officers’ own discretion. In the data compiled by rities in access to health care and mental health care, differential Selby et al. (2016), 70% of the unarmed people killed by police rates of poverty and homelessness, and differential intensities of were only encountered because they were reported to police by policing effort in different geographic locales are all candidates. other civilians as being probable threats to the community, which There are many possible and potentially overlapping reasons why PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 7 | | | ARTICLE PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z black individuals are stopped more often than white individuals, Beer T (2016) “But Blacks commit more crimes”: scholars discuss conservative logic. 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If material is not included in the Stahl J (2008) Off duty Chicago police accused of election night hate crimes. article’s Creative Commons license and your intended use is not permitted by statutory Huffington Post. http://www.huffingtonpost.com/jayne-lyn-stahl/off-duty- regulation or exceeds the permitted use, you will need to obtain permission directly from chicagopolice-a_b_142536.html the copyright holder. To view a copy of this license, visit http://creativecommons.org/ Swaine J (2014) Ferguson: officer relieved of duty after video of racist remarks licenses/by/4.0/. surfaces. The Gaurdian. http://www.theguardian.com/world/2014/aug/23/ ferguson-officerrelieved-duty-video-racist-remarks © The Author(s) 2018 PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 9 | | | http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Palgrave Communications Springer Journals

Resolution of apparent paradoxes in the race-specific frequency of use-of-force by police

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Abstract

ARTICLE DOI: 10.1057/s41599-018-0110-z OPEN Resolution of apparent paradoxes in the race- specific frequency of use-of-force by police 1 2 1 Cody T. Ross , Bruce Winterhalder & Richard McElreath ABSTRACT Analyses of racial disparities in police use-of-force against unarmed individuals are central to public policy interventions; however, recent studies have come to apparently paradoxical findings concerning the existence and form of such disparities. Although anti- black racial disparities in U.S. police shootings have been consistently documented at the population level, new work has suggested that racial disparities in encounter-conditional use of lethal force by police are reversed relative to expectations, with police being more likely to: (1) shoot white relative to black individuals, and (2) use non-lethal as opposed to lethal force on black relative to white individuals. Encounter- and use-of-force-conditional results, how- ever, can be misleading if the rates with which police encounter and use non-lethal force vary across officers and depend on suspect race. We find that all currently described empirical patterns in the structuring of police use-of-force—including the “reversed” racial disparities in encounter-conditional use of lethal force—are explainable under a generative model in which there are consistent and systemic biases against black individuals. If even a small subset of police more frequently encounter and use non-lethal force against black individuals than white individuals, then analyses of pooled encounter-conditional data can fail to correctly detect racial disparities in the use of lethal force. In more technical terms, statistical assessments of racial disparities conditioned on problematic intermediate variables, such as encounters, which might themselves be a causal outcome of racial bias, can produce mis- leading inferences. Population-level measures of use-of-force by police are more robust indicators of the overall severity of racial disparities than encounter-conditional measures— since the later neglect the differential morbidity and mortality arising from differential encounter rates. As such, population-level measures should be used when evaluating the local-level public health implications of racial disparities in police use-of-force. Research on encounter-conditional use-of-force by police can also fruitfully contribute to public policy discussions, since population-level measures alone cannot address whether racial disparities are driven by disparities in encounters or disparities in use-of-force conditional on encoun- ters. Tests for racial biases in the encounter-conditional use of lethal force, however, must account for individual-level variation across officers in terms of race-specific encounter rates or risk falling to Simpson’s paradox. 1 2 Department of Human Behavior, Ecology and Culture. Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany. Department of Anthropology, University of California, Davis, USA. Correspondence and requests for materials should be addressed to C.T.R. (email: cody_ross@eva.mpg.de) PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 1 | | | 1234567890():,; ARTICLE PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z Introduction Table 1 Population-level police shooting data (as wo recent publications on anti-black, racial disparities in proportions by race/ethnicity) from Ross (2015) and Fryer police shootings in the United States—Ross (2015) and (2016, p. 14) TFryer (2016)—have received media attention (e.g., Cox, 2016; Li, 2016; DeVega, 2016), in part because they appear to Source Armed status Black Hispanic White reach opposite conclusions concerning police behavior. Ross US Census – 0.13 0.29 0.58 (2015) shows that at the population-level individuals are about 3.5 (2010) times more likely to be black, unarmed, and shot-by-police, than Fryer (2016) All shootings 0.46 0.30 0.24 white, unarmed, and shot-by-police, adjusting for relative dif- Ross (2015) All shootings 0.38 0.38 0.24 ferences in population size. Fryer (2016), however, finds that Ross (2015) Unarmed 0.36 0.38 0.26 conditional on being encountered by police, black civilians relative individuals to white civilians are less likely to be shot by police. Such To increase comparability to the Fryer (2016) study, census data and the police shootings data apparently conflicting results have generated confusion in the from Ross (2015) have been taken only from counties where Fryer (2016) also had data. These public presentation of these two studies. The key difference counties are: Dallas, TX; Harris, TX; Travis, TX; Suffolk, MA; Camden, NJ; Pinellas, FL; Lee, FL; Orange, FL; Palm Beach, FL; Duval, FL; Brevard, FL; and Los Angeles, CA. The population data between them, however, is that Ross (2015) looks at population- show that in these counties, about 13% of residents are black, 29% of residents are of Hispanic level relative risk, whereas Fryer (2016) looks at relative risk origin, and 58% of residents are white. When considering the proportion of police shooting victims by race, the data from Fryer (2016) and Ross (2015) are very similar; both studies find conditional on encounters or use-of-force. These studies thus tell that black individuals are killed by police in greater proportions than would be expected given us different things; failure to detect racial disparities in police their race-specific population levels shootings conditional on encounters does not imply absence of racial disparities in police shootings at the population level. Even conditional rates of the use of lethal force by police may arise in light of the well-acknowledged shortcomings in the data used not from bias against white individuals, but rather from elevated in each of these studies, each exposes complementary elements of rates of unjustifiable encounters with black individuals. In order a coherent picture of the dynamics of police use-of-force. to disentangle which of these possibilities best explains the In order to gain a more fine-grained understanding of why the empirical data, future research will need to better account for encounter-conditional results of Fryer (2016) seem to run so variation across officers in terms of: (1) their race-specific, contrary to what might be expected given the population-level exposure-time conditional encounter rates with civilians, (2) their findings of Ross (2015), we derive a generative model of police race-specific, exposure-time conditional rates of use-of-force, and use-of-force outcomes, and then analyze the conditions under (3) their race-specific probabilities of use-of-force conditional on which this model can generate data consistent with both analyses. encounter. We use both analytic and simulation methods to draw attention to some counter-intuitive properties of this model. Specifically, we draw a parallel to classic findings on Simpson’s Paradox in Population-level analyses. In Table 1 we present comparable, applied statistics (Simpson, 1951; Bickel et al., 1975; Pearl, 2014), population-level data from Ross (2015) and Fryer (2016); the and demonstrate that pooled analyses of encounter-conditional outcomes are very similar. Both studies find that black individuals data—as in Fryer (2016)—will fail to find true encounter- are killed by police in greater proportions than would be expected conditional anti-black racial disparities over a wide range of given their relative population size. In fact, the data mobilized by parameter values when there is heterogeneity in the rates with Fryer (2016) show greater evidence of racial disparities in police 46% = 3.5x, than do the data which police encounter and use non-lethal force as a function of shootings at the population level: 13% 38% suspect race. For example, if even a small subset of police have presented by Ross (2015) in comparable counties: = 2.9x. See 13% propensities to more frequently encounter black relative to white also a similar comparison including data from The Guardian, The individuals, then analyses of pooled encounter-conditional data Washington Post, and VICE (Fryer, 2017). Hispanic individuals will fail to detect systemic anti-black racial disparities in the are shot in direct proportion to their population levels in the data 30% encounter-conditional use of lethal force by the larger subset of provided by Fryer (2016): = 1.0x, and at rates slightly above 30% 38% police. Likewise, if even a small subset of police are more likely to their population levels in the data provided by Ross (2015): = 30% non-lethally assault black individuals than white individuals— 1.3x. Finally, both studies agree numerically that white indivi- e.g., with tasers—in contexts when such force is not actually duals are shot at a rate less than that which would be expected 24% justified, and then report that such force was justified, analyses of given their population levels: = 0.4x, despite the fact the 58% pooled use-of-force-conditional data will suggest that lethal force authors use different data collection methodologies over different is more likely to be used against white relative to black time intervals. As such, the analyses of Ross (2015) and Fryer individuals. (2016) are in general agreement concerning the existence and In the analysis that follows, we demonstrate three important magnitude of population-level racial disparities in police conclusions: (1) Ross (2015) and Fryer (2016) document quan- shootings. titatively similar population-level anti-black racial disparities in The Ross (2015) analysis is resolved to the level of county, and the use of lethal force by police, (2) analyses of encounter- shows significant geographical diversity in the levels of racial conditional rates of the use of lethal and non-lethal force by disparities in police shootings—variation that has the potential to police are insufficient to address predictions about racial dis- advance explanations of the locally contextualized causes of police parities in policing, since they neglect the relative risk of being shootings and to identify the locales that may benefit most from encountered by police in the production equation of population- policy review. However, Ross (2015) has no data on race-specific level racial disparities; and, most critically, (3) the findings of encounter rates between police and civilians and therefore cannot Fryer (2016) suggesting null or anti-white disparities in the address the race-specific probabilities of being shot by police encounter-conditional rates of the use of lethal force by police are conditional on being encountered by police. Fryer (2016), by actually consistent with a situation in which all police have ele- contrast, has compiled a much more detailed dataset for a more vated encounter-conditional rates of the use of lethal force against limited sample of places and departments; as such, the data black individuals, but a small subset of police encounter and provided by Fryer (2016) allow for a more thorough micro-level assault black individuals sub-lethally at elevated rates. In other analysis of the generative pathways of racial disparities in police words, apparent anti-white racial disparities in encounter- use-of-force in specific locations. 2 PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms | | | PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z ARTICLE The data in Ross (2015) could be biased by selective reporting, Ross (2015) and the encounter-contingent results of Fryer (2016), for instance were individual engaged in the crowd-sourcing effort including: to have preferentially reported police shootings of unarmed black 1. Elevated population-level rates of police encounters with civilians, rather than following the random sampling methodol- black individuals relative to white individuals—see Fryer ogy procedure requested by Wagner (2014). Likewise, the data in (2016, Table 1A, Panel A) and Fryer (2016, Table 1D, Panel Fryer (2016) could come from a biased sample of departments. A). Nevertheless, both studies show remarkably similar findings when 2. Elevated population-level rates of lethal force against black comparable, population-level measures are used. This initial individuals relative to white individuals—see Ross (2015) and comparison serves to cross-validate, to some extent, both data Fryer (2016, Table 1C, Panel A). sources for studying population-level disparities in police use-of- 3. Elevated encounter-conditional rates of non-lethal force force. against black individuals relative to white individuals—see Fryer (2016, Table 2A) and Fryer (2016, Table 2B). And the so-called paradoxes in otherwise consistent Encounter-conditional analyses. Given the general agreement of patterns: the population-level results between these two studies, at first 4. Elevated encounter-conditional rates of lethal force against pass the encounter-conditional results of Fryer (2016)are white individuals relative to black individuals—see Fryer striking. Drawing on his micro-level data, Fryer (2016) finds (2016, Table 5). consistent, strong, and significant levels of anti-black racial dis- 5. Elevated probability ratios of the use of non-lethal force to parities in police use of non-lethal force in graded categories lethal force against black individuals relative to the same ratio from hands on, to handcuffing, display of a weapon, use of against white individuals—see Fryer (2016, Table 5). pepper spray, and use of a baton. These racial disparities remain unexplained even after accounting for 112 (Fryer, 2016,p. 17) context-dependent covariates. But, in a result he describes as a Informal model description. Informally, the model we use “stark contrast to non-lethal uses of force” (p. 5), he finds that entails a homogeneous police force, and sub-populations of black use of lethal force by police actually shows reversed, anti-white, and white citizens. The model makes explicit assumptions about racial disparities; black individuals are less likely than white police behavior concerning race-specific rates of police encoun- individuals to be shot by police, conditional on being encoun- ters with citizens, and the probabilities of the use of no force, tered by police. non-lethal force, or lethal force by police conditional upon This result has been emphasized in media accounts and is encounter. The model provides a demonstration of the manner in surprising in light of general findings on racial disparities in which an apparently paradoxical result (the simultaneous truth of police use of both lethal and non-lethal force spanning several all five of the observations listed above) is fully consistent with decades and literatures—i.e., research on implicit psychological police use-of-force being systematically biased against black biases (Plant et al., 2005; Correll et al., 2006, 2007), sociological individuals. drivers of racial disparities (Jacobs, 1998; Smith, 2003; Bergesen, 1982; Gilbert and Ray, 2016), structural disparities established by Formal model description. Formally, our model assumes that we the existing social order (Harring et al., 1977; Jacobs and Britt, have a population of N individuals, with black and white sub- 1979; Holmes, 2000), proximate responses by police to areas of populations N and N , where: N = N + N . Note that we will B W B W high crime and risk (Jacobs, 1998; Fyfe, 1980), racial bias in continue to use subscripts of B and W to refer to black and white profiling and encountering individuals (Warren et al., 2006; sub-populations, and that all parameters are defined in Table 2 Tomaskovic–Devey et al., 2004; Gelman et al., 2007), blatant for ease of reference. We assume that over some interval of time, racism (Goldkamp, 1976; Martinot and Sexton, 2003; Doane, E and E individuals are encountered by police, at rates: ϕ ∈ [0, B W B 2006), and social dominance orientation (Sidanius and Pratto, 1] and ϕ ∈ [0, 1]. As such, we expect the counts of encounters to 2001), over many geographic areas: United States (Ross, 2015; follow: Hirschfield, 2015), Canada (Wortley and Tanner, 2003; Wortley E  Binomial N ; ϕ ð1Þ and Owusu–Bempah, 2012), Brazil (Cano, 2010; French, 2013), B B B and South Africa (Brogden and Shearing, 2005). Nonetheless, the widely publicized interpretation of Fryer (2016)—one that he E  Binomial N ; ϕ ð2Þ W W W himself highlights—is that police do not show anti-black racial bias in the use of lethal force. While we do not doubt that this pattern is apparent in the analyzed data, we take issue with We then assume that conditional upon encountering a civilian, interpretation, given that other aspects of Fryer’s analysis suggest police engage in the use of either no force, non-lethal force, or that Simpson’s paradox could be driving this effect (Simpson, lethal force. Let the parameters: θ ∈ [0, 1] and θ ∈ [0, 1] define B W 1951; Pearl, 2014; Bickel et al., 1975, and see Discussion). In the the probability of the use of lethal force conditional upon following sections, we show that the encounter-contingent results encounter, and the parameters: γ ∈ [0, 1−θ ] and γ ∈ [0, 1 B B W of Fryer (2016) are consistent—perhaps counter-intuitively so— −θ ]define the probability of the use of non-lethal force with systemic and consistent anti-black racial disparities in police conditional upon encounter. The probability of police using no encounter rates and in the subsequent rates of the use of both force on white and black individuals upon encounter is then given lethal and non-lethal force upon encounter. by: 1−(θ + γ ) and 1−(θ + γ ), respectively. W W B B Then, to define the counts of lethal force by police, S and S , B W and non-lethal force by police, G and G , we write: B W A generative model of racial disparities in use-of-force by ðS ; G ; O Þ′  Multinomial E ; ðθ ; γ ; 1 ðθ þ γ ÞÞ′ ð3Þ police B B B B B B B B We resolve the counter-intuitive results by using a generative model to demonstrate that increased racial disparity in the rates ðS ; G ; O Þ′  Multinomial E ; ðθ ; γ ; 1 ðθ þ γ ÞÞ′ W W W W W W W W at which a subset of police engage civilians with non-lethal force ð4Þ will generate all patterns found in the population-level results of PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 3 | | | ARTICLE PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z Table 2 Model variables and relationships. Subscripts B and W refer to black and white sub-populations, respectively Variable Definition Formula(s) Domain N Population under consideration N= N + N 2 N W B E Count of individuals subjected to a police encounter Eqs. (1) and (2), text ∈{1, …, N} S Count of lethal police actions Eqs. (3) and (4), text ∈{1, …, E} G Count of non-lethal police actions Eqs. (3) and (4), text ∈{1, …, E} ϕ Probability of encounter with police ∈[0, 1] θ Probability of receiving lethal force, conditional on encounter ∈[0, 1] γ Probability of receiving non-lethal force, conditional on encounter ∈[0, 1 − θ] ψ Population-level rate of lethal police actions ψ= ∈[0, 1] δ Population-level rate of non-lethal police actions δ = ∈[0, 1] Φ Relative population-level risk of being subjected to a police encounter Φ = ∈[0, ∞) Θ Relative risk of being the victim of a lethal police action conditional upon encounter Θ = ∈[0, ∞) Γ Relative risk by being of being the victim of a non-lethal police action conditional upon Γ= ∈[0, ∞) encounter Ψ Relative population-level risk of being the victim of a lethal police action Ψ = ∈[0, ∞) Δ Relative population-level risk of being the victim of a non-lethal police action Δ = ∈[0, ∞) The “hat” symbol used in the text indicates parameter values unique to the routine over-escalation sub-model; the parameters without the “hat” symbol refer to the standard policing model. We note that the term “non-lethal” includes sub-lethal violent engagements, but excludes non-violent engagements Table 3 Conditions for the presence or absence of racial disparities and their direction if present Form of bias Absent Present Against black individuals Against white individuals Encounter ϕ = ϕ ⇔ Φ = 1 ϕ > ϕ ⇔ Φ >1 ϕ < ϕ ⇔ Φ <1 B W B W B W Population-level, non-lethal force δ = δ ⇔ Δ = 1 δ > δ ⇔ Δ >1 δB < δ ⇔ Δ <1 B W B W W Population-level, lethal force ψ = ψ ⇔ Ψ = 1 ψ > ψ ⇔ Ψ >1 ψ < ψ ⇔ Ψ <1 B W B W B W Encounter-conditional, non-lethal force γ = γ ⇔ Γ= 1 γ > γ ⇔ Γ >1 γ < γ ⇔ Γ <1 B W B W B W Encounter-conditional, lethal force θ = θ ⇔ Θ = 1 θ > θ ⇔ Θ >1 θ < θ ⇔ Θ <1 B W B W B W Variables are defined in Table 2; the double arrow (⇔) is read as “is equivalent to” where: O = E −(S + G ) and O = E −(S + G ), meaning and encounter-conditional use of non-lethal and lethal force (see B B B B W W W W that the outcome vectors contain the predicted counts of lethal Table 3). force, non-lethal force, and no force, given the number of For example, we would consider disparity in encounters to be encounters and the probability parameters for each use-of-force absent if race-specific rates of encounters are equal: ϕ = ϕ . This B W category. is the same as saying that the relative risk of encounter by race is Finally, we can write the total population-level rates of the use equal to one: Φ = 1, or that the log of this value is equal to zero: S S of lethal force as: ψ = B= and ψ = W= , and the total log(Φ) = 0. We would consider encounters to be structured N N B W B W population-level rates of non-lethal force as: δ = = and δ = against black individuals if: ϕ > ϕ , or equivalently if: Φ >1, or B N W B W W= . The population-level relative risk of being the victim of a finally, if: log(Φ) > 0. Reversing the inequalities would indicate lethal police action, Ψ, is then given as: Ψ = B= . The disparities against white individuals. The remaining four types of population-level relative risk of being the victim of a violent disparities are described in the same fashion. but non-lethal police action, Δ, is given as: Δ = B= . The relative risk of being encountered by police, Φ,isdefined as: Φ = B= . The standard policing model. We name the full generative The relative risk of being the victim of a lethal police action model described above the standard policing model, and take it to conditional on being encountered by police, Θ, is given as: Θ = define the universe of standard police interactions, although there B= . The relative risk of being the victim of a violent but non- W may be either unjustifiable (implicit or explicit bias) or justifiable lethal police action conditional on being encountered by police, Γ, (a response to crime) racial disparities in the rates of encounters is given as: Γ = B= . W or use-of-force in this model. At this point, we note a key dependency in the model. The overall counts of lethal and non-lethal force depend on the rates Assessing sources of disparities.Wedefine racial disparities as of encounters given by ϕ and ϕ , via the counts E and E . This W B W B the disproportionate representation of a racial sub-group in a gives us our first insight on the apparent paradox that population- particular type of police action category. That is, we seek here to level analyses of U.S. data show anti-black racial disparities in avoid any prejudicial connotations of the term, as we do not police shootings, while encounter-contingent analyses show know, or need to know for the narrow purposes of our analysis, if reversed, anti-white disparities. A difference in race-specific such disparities are justifiable in some manner or not. We encounter rates could lead to population-level racial disparities in recognize five ways in which racial disparities may occur or be police shootings, even in the absence of racial disparities in police documented as absent: in encounters, and in the population-level shootings conditional on encounter. 4 PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms | | | PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z ARTICLE ^ ^ More formally, the log of the expected population-level extent parameters: ϕ 2½0; 1 and ϕ 2½0; 1. As such, we expect the B W of racial disparities in police shootings is approximately: counts of these encounters to follow: _ ð6Þ E  BinomialðN ; ϕ Þ logðE½ΨÞ  logðΘÞþ logðΦÞð5Þ B B B for N sufficiently large and θ ϕ not too small (see ^ ^ ð7Þ W W W E  BinomialðN ; ϕ Þ W W Supplementary Materials for derivation). Even if police are more likely to use lethal force against white people than black people The counts of lethal and non-lethal force events resulting from conditional on encounter (i.e., log(Θ) < 0, which might be these interactions are then given by: expected if police preferentially encounter white individuals ^ ^ ^ ^ ^ ^ ðS ; G ; O Þ′  MultinomialðE ; ðθ ;^γ ; 1 ðθ þ ^γ ÞÞ′Þ ð8Þ B B B B B B B B engaging in crimes, but encounter black individuals more frequently or haphazardly), then we will still see population- level anti-black racial disparities in police shootings on average so ^ ^ ^ ^ ^ ^ ðS ; G ; O Þ′  MultinomialðE ; ðθ ;^γ ; 1 ðθ þ ^γ ÞÞ′Þ W W W W W W W W long as the relative risk of encounters (i.e., log(Φ)) is large enough ð9Þ to compensate. This might also occur if the threshold of suspicion leading to an encounter is lower for black individuals than for ^ ^ ^ ^ ^ ^ ^ ^ where O ¼ E ðS þ G Þ and O ¼ E ðS þ G Þ. Equa- B B B B W W W W white individuals. Note also that the final population-level metric tions (6), (7), (8), and (9) are of the same form as Eqs. (1), (2), (3), is the more appropriate indicator of the public health issue at and (4) in the standard policing model. The parameters also are hand; regardless of whether differential rates of encounters or the same in definition, with the “hat” symbol indicating that they differential use-of-force conditional on encounters drives differ- refer to the routine over-escalation model and can take on ential morbidity and mortality rates, the end result is the same— different values than in the standard policing model. The logical greater overall morbidity and mortality from police per unit conditions establishing the presence or absence of racial population. This being said, the results of Fryer (2016)—should disparities in this model are the same as those given in Table 3. they replicate under individual-level analyses that control for the If the population of officers is composed of some police possible dynamics discussed in this paper—provide the key operating under the standard parameters, and some operating insight that reduction in population-level racial disparities in under the routine over-escalation parameters, then the joint police use-of-force might depend more on attenuation of racial mixture model is able to produce the aggregate appearance of disparities in encounter rates than on changes in how officers anti-white disparities in lethal force conditional on encounter respond to suspects conditional on their race. ^ ^ S þS S þS B B W W (i.e., < ), even when there are no anti-white racial ^ ^ E þE E þE B B W W The routine over-escalation model. The above result suggests disparities in the use of lethal force conditional on encounter in ^ ^ that sub-structure in the behavioral patterns of police which S S S S B W B W either subgroup of police (i.e., > and > ). The easiest ^ ^ E E B W E E increases their rate of non-lethal encounters with black indivi- B W S S B W sufficient condition to understand arises when set ¼ λ, with duals will have the effect of diminishing the apparent rate of lethal E E B W outcomes conditional on encounters, while leaving the λ > 1, and then make the assumption that the count of lethal force population-level rates of racial disparities in police shootings incidents against white individuals in the routine over-escalation unchanged. To formally explore this idea, we introduce a second sub-model declines to zero (i.e., S ! 0). Even under these generative model below. conditions, we show (in the Supplementary Materials) that this Assume that there is heterogeneity in the types of encounters model produces an apparent absence of encounter-conditional with police—e.g., i) those resulting from police operating under anti-black racial disparities—actually anti-white racial disparities standard protocols and ii) those resulting from police engaging in —in the use of lethal force whenever: more routine and excessive use of non-lethal force. If this is the E E B W case, then the probability that white individuals will be more λ < ð10Þ ^ ^ likely than black individuals to receive lethal force conditional on ðE þ E Þ ðE þ E Þ B B W W encounter grows as the small subset of police that engage in excessive use of non-lethal force target black people at increasing This expression indicates that as long as there are sufficient rates. This effect holds even when all parameter values (i.e., anti-black racial disparities in the frequency of encounters arising encounter rates, and rates of the use of lethal and non-lethal force from the routine over-escalation model to offset the anti-black conditional on encounter) are structured against black individuals racial disparities in the use of force conditional on encounter in in both subsets of police officers. the standard policing model, we will observe an apparent absence We demonstrate this result by defining an additional sub-model, of anti-black disparities in the use of lethal force conditional on the routine over-escalation model. In this model, some small subset encounter in the pooled data. In the language of the model, if E of police officers are more prone to engage in additional illegitimate is sufficiently large relative to other terms, then it can offset a λ > and unnecessary encounters with individuals. While it is not 1. For example, if the encounter-conditional black to white necessary to provide a reason for why we might see such relative risk of being shot by police were λ = 1.11, then if just 1 in heterogeneity in officer propensities, a body of research in social 20 white encounters, but 3 in 20 black encounters occur under the dominance theory (e.g., Sidanius et al., 1994; Sidanius and Pratto, routine over-escalation model, we would still—perhaps para- 2001) provides some coherent explanations. Since the individuals doxically—see aggregate-level anti-white racial disparities in encountered in these cases are not necessarily encountered on encounter-conditional use of lethal force by police. reasonable suspicion of a crime, we assume that use of lethal force conditional on encounter is less likely than under the standard policing model, butthatuse of non-lethal forceiselevated. Implications of our model for statistical analysis of police We assume that over the same interval of time as in the shooting data. To emphasize the implications of our findings for ^ ^ standard policing model, E and E individuals in each respective empirical analyses, we present in the Supplementary Materials an B W sub-population get encountered by the subset of police who additional analysis in which we simulate data on police encoun- engage in excessive use of non-lethal force, at rates given by the ters under the union of the standard policing and routine over- PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 5 | | | ARTICLE PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z escalation models. We then analyze the aggregate data with a complete reversal in encounter-conditional rates of lethal force. statistical model that ignores the fact that the use-of-force out- Our model results, however, establish that precisely this set of comes arise through a generative model structure with hetero- racial disparities in rates of encounters and use of non-lethal force geneous decision making units (i.e., the above-listed sub-types of can lead to the principle finding of Fryer (2016). police officers). The results again confirm that the “paradoxical” Our findings parallel classic results in applied statistics related results with which we began are only apparent. Furthermore, we to Simpson’s paradox (e.g., Simpson, 1951; Bickel et al., 1975); show that a wide range of parameter values are sufficient to analysis of aggregate data (i.e., data arising from pooling the produce the seemingly paradoxical results and demonstrate that outcomes of heterogeneous decision-making units) can show the phenomenon does not strongly depend on the particular discrimination against a given class of individuals, even when reducing assumptions used to reach an analytical solution. there is actually discrimination in the opposite direction in every decision-making unit. Disparities in the rates with which indivi- duals interact with each decision-making unit are typically found Discussion in cases where Simpson’s paradox is demonstrated. For example, The data and methodological approach presented in Fryer (2016) in the case of the Berkeley graduate admissions data (Bickel et al., represent the most important advance to date in the analysis of 1975), women tended to apply to departments that were more race-specific of use-of-force by police. Fryer (2016) is able to difficult for applicants of either sex to enter, while men tended to investigate aspects of police use-of-force (like encounter-condi- apply to departments that accepted a greater majority of appli- tional, race-specific rates of the use of lethal force) that have thus cants of either sex; as a result, in the aggregate, men were accepted far been opaque. However, this new ground brings with it some in greater proportion than women, despite the fact that there was counter-intuitive terrain for analysts and for the journalists who actually evidence of a small average bias in admitting women at summarize research for the public. Specifically, we show that the the level of the decision-making unit. presentation of Fryer’s results as indicating an absence of anti- The case of racial disparities in police shootings conditional on black racial disparities and perhaps even the presence of anti- encounter holds a similar logical structure. However, the variable white racial disparities in police use of lethal force is unwarranted. that structures decision-making (akin to the academic depart- Both Ross (2015) and Fryer (2016) show population-level anti- ment in the Berkeley graduate admissions data) is much harder to black racial disparities in the use of lethal force by police—dis- empirically identify in the case of police shootings. We show that parities that are indicative of disproportionate morbidity and racial disparities in encounter rates can generate Simpson’s mortality per unit population. The theoretical model presented paradox, and we provide an example of a kind of decision- here allows us to decompose these disparities into the effects of structuring variable (whether a given officer has standard policing differential encounters and differential the use of lethal force or routine over-escalation parameters) which produces model conditional on encounters. Either of these statistical biases may be outcomes that are similar to the empirically observed data. It will justifiable on the basis of differential crime rates or con- likely be difficult to empirically evaluate if Simpson’s paradox textualizing details. The narrow objective of our analysis, how- truly explains the results of Fryer (2016) since the longitudinal, ever, does not require we take a position as to whether or not individual-level data needed to estimate more finely-resolved differential encounters and differential use of force are justified. model parameters will be very hard to acquire. Nonetheless, this Nonetheless, the existence of population-level disparities in police point is largely eclipsed by a more important point—namely, that use-of-force raises social and policy issues that must be addressed. the public health implications of racial disparities in police Taking the analysis of Fryer (2016, 2017) at face value, it would shootings and non-lethal use-of-force (e.g., Miller et al. 2017; appear that race-based differences in the use of lethal force con- DeVylder et al., 2017; Ross, 2017), in the end, come down to the ditional on encounter can be entirely explained by contextualizing population-level relative risk not the encounter-conditional risk. details. But, as we show, if police behavior is heterogeneous, with most officers following standard protocol and a small subset of officers engaging in unwarranted use of excessive non-lethal force Pathways leading to population-level racial disparities in police (like use of tasers), racial disparities in who this subset of officers use-of-force. While the use of lethal force against unarmed target can complicate interpretation of encounter-conditional individuals by police is quite rare, it does occur and with racial data. It is ironic that elevated levels of sub-lethal assault against disparities in population-level rates. Non-lethal force also is dis- innocent black individuals by a subset of police would have the proportionate at the population level (Fryer, 2016; Miller et al., effect of diminishing the apparent severity of anti-black racial 2017). These observations are not contradicted by the observation disparities in lethal force conditional on encounter in the full set of that the encounter-conditional probabilities of lethal outcomes by officers. Nevertheless, this is a key finding of our model. Increased race are reversed in aggregate data. While Fryer (2016) and Ross encounter rates and excessive use of violent but non-lethal force (2015) address somewhat different questions, each using variables by a subset of police against black individuals can mask the unique to their datasets, they arrive at complementary, not existence of anti-black racial disparities in the encounter- paradoxical, conclusions. Those conclusions reinforce the pre- conditional use of lethal force by police in pooled data. vailing consensus that there are significant racial disparities in Given that the existence of racial disparities in police use-of- police behavior at the population level, and together they provide force is a serious public policy issue (e.g., USDOJ, 2016), it is an expanded basis for appreciating that this is a complex problem critical that these dynamics be understood. Although the work of at the local level Fryer (2016), with significant differences among Fryer (2016) presents one of the most detailed empirical analyses locales nationally Ross (2015). of racial disparities in police use-of-force, only individual-level Within each locale, the research strategy advanced by Fryer estimates of officer parameters will allow a convincing demon- (2016)isimportant,asitallows ustomovebeyond simply stration of his arguments. Though it is impossible to demonstrate demonstrating the presence of disparities and instead investigate strictly though our modeling effort here, it seems improbable that how and why such disparities arise when and where they do. there would be such consistent evidence of racial disparities in Without being able to identify the causal drivers of racial disparities rates of: (i) encounters with police, (ii) population-level and operating in a given location we are unable to offer useful policy encounter-conditional use of non-lethal force by police, and (iii) recommendations (Ross, 2016). It is important to determine if racial population-level use of lethal force by police, only to see a disparities in a particular locale arise due to officer behavior 6 PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms | | | PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z ARTICLE conditional on encounter, or via the policies and social contexts the police were obliged to investigate, often after being primed leading to racial disparities in encounter rates. The combination of that the indicated persons posed a threat. explicit theoretical modeling of the generative pathways of use-of- Black Americans are disproportionately likely to be encoun- force outcomes, wariness concerning Simpson’sparadox,and mixed tered by police, be the victims of violent but non-lethal use-of- use of both qualitative and quantitative methods will help force by police, and be the victims of lethal use-of-force by police. researchers better understand the empirical data. However, these observations are fully consistent with the observation that the great majority of individual officers do not Officer behavior. Police officers and police departments are disproportionately target black people based on their own diverse, and it is inappropriate to characterize such institutions in personal discretion and do not show racial bias in the use of monolithic terms. There is no shortage of cases of police officers lethal or non-lethal force conditional on encountering a given engaging in overt racism in recent years (e.g., cases in Los individual. Social context is likely to play a significant role in Angeles, (Stack, 2016; Whaley, 2013), Oakland, CA (Shoichet explaining differential encounter rates and their downstream et al., 2016), San Francisco, CA (Serna and Romney, 2015; Serna, effects on population-level racial disparities in police use-of-force. 2016), San Diego, CA (Perry, 2015), Miami, FL (Buncombe, 2015), Fort Lauderdale, FL (Barszewski, 2016), Clatskanie, OR Social context, policies, and encounter rates. Recent data show that (Park, 2015), Seattle, WA (Campbell, 2015), New York, NY black individuals are more likely to be stopped by police than (Sapien, 2015), Camden, NJ (Walsh, 2016), Edison, NJ (Amaral, white individuals (Fryer, 2016; Miller et al., 2017; USDOJ, 2016). 2015), Ferguson, MO (Swaine, 2014), Saint Louis, MO (Hudson, Miller et al. (2017) argue that the differential population-level 2014), Cleveland, OH (Hensley, 2014), Detroit, MI (Murphy, rates of the use of lethal force by police are almost entirely 2013), New Orleans, LA (McCarthy, 2012), Baton Rouge, LA explainable by these disparities in encounters—an interpretation (Alejandro, 2014), Chicago, IL (Stahl, 2008), Baltimore, MD which is not inconsistent with our present analysis. There are two (USDOJ, 2016), and other locations). Excessive media and public major lines of argument concerning the causes of differential focus on the sensationalized cases mentioned above, however, has encounter rates: (1) that differential encounter rates are driven by the potential to wrongfully impute such attitudes to police officers differential rates of crime, and (2) that the ‘criminalization of in general, trigger in-group out-group identity politics, and to blackness’ leads to racial disparities in encounters for reasons distract from the dialog needed to implement effective policies having little to do with differential crime rates. addressing the problem. While is important to end impunity for In the aggregate in the United States, there appear to be higher the small subset of officers who abuse their positions of power per capita rates of violent crime committed by black individuals and responsibility, or display outward signs of racist hatred like relative to white individuals (e.g., USDOJ, 2014)—the caveat is some of those mentioned above, it is also important to identify that these arrest/conviction records may themselves be an the less visible, institutional drivers of racial disparities in police outcome of racial disparities in policing intensity and conviction use-of-force. rates. But, there is no evidence to suggest that the counties with There is increasing evidence that the population-level presence relatively high black to white crime rate ratios are those with of racial disparities in police shootings might have less to do on disproportionally high rates of racial disparities in police use of average with officer behavior conditional on encounter, and more lethal force against unarmed individuals (Ross 2015); however, to do with differences in encounter rates (Fryer, 2016; Miller the analysis of Ross (2015) linking county-level crime rates and et al., 2017. This information may be key to creating more racial disparities in police shootings is itself very susceptible to the effective policy change. Selby et al. (2016) have compiled a ecological inference fallacy. This being said, other more detailed, detailed data set of officer caused deaths of unarmed individuals geographically localized studies have also found racial disparities in the United States in 2015. At the population level, their data in rates of encounters and use-of-force that are not fully closely echo those of Ross (2015) and Fryer (2016)—black explainable by differential crime rates or related variables (e.g., individuals represent about 42% of the victims of known race, Fryer, 2016; Gelman et al. 2007; USDOJ, 2016). 42% despite being only about 12% of the population ( = 3.5x), Explanations for differential encounter rates based on the 12% while non-Hispanic white individuals represent about 39% of the 'criminalization of blackness' tend to hold strong narrative weight victims of known race, but make up about 62% of the population but are more difficult to confirm with empirical data. The 39% ( = 0.63x). Selby et al. (2016), however, investigate the principle idea is that black individuals are more likely to be 62% contextualizing details of each case, and find that there is no reported by community members to the police than white evidence to suggest that overt or even unconscious racial individuals—especially in socio-economically unequal areas—for prejudice plays a systematic role in the officer-involved deaths innocuous activities like smoking a cigarette at night, jogging, of unarmed citizens—which is not to say that cases to the walking or driving in ‘the wrong kind of neighborhood’, wearing contrary never occur. Instead, their findings point to other hoodie-style sweat shirts, driving nice cars, driving not-so-nice characteristics associated with the victim, including acute drug cars, etc. (Beer, 2016); there is a body of qualitative literature of intoxication, mental and physical illness, violent behavior, and this topic, and arguments linking community behaviors and perceived threats to innocent civilians as being critical predictors biases in the representations of black people by the U.S. media of the deaths of unarmed civilians due to police intervention (see further discussion in the Supplementary Materials). How- (Selby et al. 2016). Further, Selby et al. (2016) and Ross (2015) ever, fine-grained, geographically representative quantitative data both note that most civilians who are shot by police were armed on the disproportionate rates at which black individuals are at the time of the incident. reported to the police for innocuous activities appear to be Additionally, Selby et al. (2016) mention that in about 88% of unavailable. Production of this kind of data would be a fruitful the lethal police encounters not beginning with traffic stops, direction for future research. officers engage suspects only after being requested to do so by the Other dynamics might lead to disproportionately high rates of community (i.e., via 911 calls). As such, these encounters are not encounters between black individuals and police. Racial dispa- initiated at the officers’ own discretion. In the data compiled by rities in access to health care and mental health care, differential Selby et al. (2016), 70% of the unarmed people killed by police rates of poverty and homelessness, and differential intensities of were only encountered because they were reported to police by policing effort in different geographic locales are all candidates. other civilians as being probable threats to the community, which There are many possible and potentially overlapping reasons why PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 7 | | | ARTICLE PALGRAVE COMMUNICATIONS | DOI: 10.1057/s41599-018-0110-z black individuals are stopped more often than white individuals, Beer T (2016) “But Blacks commit more crimes”: scholars discuss conservative logic. Sociology Toolbox. https://thesocietypages.org/toolbox/blacks_commit_ and these reasons are likely to be variable in space and time. more_crimes_1/ Successful policy interventions are likely to require local-level Bergesen A (1982) Race riots of 1967: an analysis of police violence in Detroit and investigation, and should be adaptive to the shifting circum- Newark. J Black Stud 12(3): 261–274. stances affecting local communities. Bickel PJ, Hammel EA, O’Connell JW et al. (1975) Sex bias in graduate admissions: data from berkeley. Science 187(4175):398–404 Brogden M, Shearing CD (2005) Policing for a new South Africa. Routledge, Conclusions London and New York We establish that: (1) the analyses of Ross (2015) and Fryer Buncombe A (2015) Miami beach cops sent more than 200 racist, homophobic and (2016) are in general agreement concerning the existence and pornographic emails, says senior officer: probe launched amid concerns magnitude of population-level anti-black, racial disparities in hundreds of criminal prosecutions could be jeopardised. Independent. http:// police shootings; (2) because of racial disparities in rates of www.independent.co.uk/news/world/americas/miami-beach-copssent-more- than-200-racist-homophobic-and-pornographic-emails-sayssenior-officer- encounters and non-lethal use-of-force, the encounter- 10255914.html conditional results of Fryer (2016) regarding the relative fre- Campbell A (2015) Police officer fired for racial bias after falsely claiming Black quency of the use of lethal force by police are susceptible to man attacked her with golf club. The Huffington Post. http://www. Simpson’s paradox. They should probably not be interpreted as huffingtonpost.com/entry/officer-fired-racial-bias-golfclub- providing support for the idea that police show no anti-black bias cane_us_55f9a334e4b0e333e54c2d56 Cano I (2010) Racial bias in police use of lethal force in Brazil. Police Pract Res 11 or even an unexpected anti-white bias in the use of lethal force (1):31–43 conditional on encounter; and, (3) even if police do not show Correll J, Park B, Judd CM, Wittenbrink B, Sadler MS, Keesee T (2007) Across the racial bias in the use of lethal force conditional on encounter, thin blue line: police officers and racial bias in the decision to shoot. J Pers racial disparities in encounters themselves will still produce racial Soc Psychol 92(6):1006 disparities in the population-level rates of the use of lethal force, a Correll J, Urland GR, Ito TA (2006) Event-related potentials and the decision to shoot: the role of threat perception and cognitive control. J Exp Soc Psychol matter of deep concern to the communities affected. 42(1):120–128 These findings have specific public policy implications: (1) Cox A (2016) Roland Fryer answers reader questions about his police force study. population-level measures of the use of lethal and non-lethal The New York Times. http://www.nytimes.com/2016/07/13/upshot/roland- force by police are more robust indicators of the overall severity fryer-answers-reader-questions-about-his-police-force-study.html of racial disparities in use-of-force by police than encounter- DeVega C (2016) Sorry conservatives, new research from Harvard shows a pro- found amount of racism by police…not less of it. Salon 26 (5):466–477. conditional measures. Population-level results should thus be http://www.salon.com/2016/07/14/ used when evaluating the local-level public health implications of sorry_conservatives_new_research_from_harvard_shows_a_profound_a- racial disparities in police use-of-force. We can improve our mount_of_racism_by_policenot_less_of_it/ understanding of the broader effects of racial disparities in police DeVylder JE, Oh HY, Nam B, Sharpe TL, Lehmann M, Link BG (2017) Prevalence, use-of-force if we avoid assessments conditioned on problematic demographic variation and psychological correlates of exposure to police victimisation in four US cities. Epidemiol Psychiatr Sci 26(5):466–477 intermediate variables such as encounters, which might occur for Doane A (2006) What is racism? Racial discourse and racial politics. 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Cambridge University Press, Cambridge and New York Simpson EH (1951) The interpretation of interaction in contingency tables. J Royal Open Access This article is licensed under a Creative Commons Stat Soc B: 13(2):238–241 Attribution 4.0 International License, which permits use, sharing, Smith BW (2003) The impact of police officer diversity on police-caused homi- adaptation, distribution and reproduction in any medium or format, as long as you give cides. Policy Stud J 31(2):147–162 appropriate credit to the original author(s) and the source, provide a link to the Creative Stack L (2016) Los Angeles police official resigns over racist emails. New York Commons license, and indicate if changes were made. The images or other third party Times. http://www.nytimes.com/2016/05/02/us/los-angeles-police-official material in this article are included in the article’s Creative Commons license, unless resigns-over-racist-emails.html?_r=0 indicated otherwise in a credit line to the material. If material is not included in the Stahl J (2008) Off duty Chicago police accused of election night hate crimes. article’s Creative Commons license and your intended use is not permitted by statutory Huffington Post. http://www.huffingtonpost.com/jayne-lyn-stahl/off-duty- regulation or exceeds the permitted use, you will need to obtain permission directly from chicagopolice-a_b_142536.html the copyright holder. To view a copy of this license, visit http://creativecommons.org/ Swaine J (2014) Ferguson: officer relieved of duty after video of racist remarks licenses/by/4.0/. surfaces. The Gaurdian. http://www.theguardian.com/world/2014/aug/23/ ferguson-officerrelieved-duty-video-racist-remarks © The Author(s) 2018 PALGRAVE COMMUNICATIONS (2018) 4:61 DOI: 10.1057/s41599-018-0110-z www.nature.com/palcomms 9 | | |

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