Consensus measures for various informational bases.
Three new proposals and two case studies from political
Carlos R. Alcantud
Published online: 16 January 2016
Ó Springer Science+Business Media Dordrecht 2016
Abstract We study consensus measures that quantify the cohesiveness of the information
generated when a group of decision-makers express their evaluations of a number of issues.
Particularly, in social choice an approval consensus measure (ACM) is used to evaluate the
degree of cohesiveness in a group of agents that have dichotomous opinions on the issues.
In this paper we propose three novel consensus indexes that take advantage of the speciﬁc
information about such opinions: namely, the Herﬁndahl–Hirschman ACM, the majori-
tarian ACM and the weighted majoritarian ACM. To illustrate their performance we apply
them to the analysis of popular votes in Switzerland and Italy. The ﬁrst analysis has a ﬁxed
population of agents (the cantons) and all votes are known. In the second analysis we have
a variable population (the voters) and unknown individual votes. In both real case studies,
we show empirical evidence that the new indexes can be used to assess consensus.
Keywords Consensus measure Á Diversity index Á Political consensus
Since Shannon (1948) originally proposed an index to evaluate the information content or
entropy in strings of texts, many other proposals attempted to measure diversity in infor-
mation or populations. It has often been the case that the same index has been developed in
different applicable ﬁelds like ecology, ﬁnance, linguistics, et cetera. For example, the
Carlos R. Alcantud
BORDA Research Unit and IME, Universidad de Salamanca, 37007 Salamanca, Spain
Facultad de CC Econo
micas y Empresariales, Universidad de Almerı
a, La Can
ada de San Urbano
s.n., 04120 Almerı
Qual Quant (2017) 51:285–306