Pairwise Dichotomous Cohesiveness Measures

In a framework where experts or agents express their opinions in a dichotomous way, we analyze the cohesiveness of their opinions on a fixed set of issues in a population. A parametric family of related measures are introduced and axiomatically characterized. They are ordinally equivalent when the population is fixed, and some further properties are proved. In order to argue that this restricted dichotomous situation is nevertheless versatile, the paper ends with several empirical illustrations based on real forecasts (for the 2012 American presidential election) and elections (with real data from referenda in two countries and from elections in several scientific societies).

[1]  C. F. Kossack,et al.  Rank Correlation Methods , 1949 .

[2]  William L. Hays.  A Note on Average Tau as a Measure of Concordance , 1960 .

[3]  D. Knuth,et al.  Mathematics for the Analysis of Algorithms , 1999 .

[4]  Peter C. Fishburn,et al.  Going from theory to practice: the mixed success of approval voting , 2005, Soc. Choice Welf..

[5]  R. Bosch.  Characterizations on voting rules and consensus measures , 2006 .

[6]  Steven J. Brams,et al.  Dead Heat: The 2006 Public Choice Society Election , 2006 .

[7]  Francisco Herrera,et al.  Group decision making with incomplete fuzzy linguistic preference relations , 2009, Int. J. Intell. Syst..

[8]  Enrique Herrera-Viedma,et al.  Consensual Processes , 2011, Studies in Fuzziness and Soft Computing.

[9]  Dinko Dimitrov,et al.  The Social Choice Approach to Group Identification , 2011, Consensual Processes.

[10]  Jorge Alcalde-Unzu,et al.  Measuring the cohesiveness of preferences: an axiomatic analysis , 2013, Soc. Choice Welf..

[11]  Biung-Ghi Ju.  On the characterization of liberalism by Samet and Schmeidler , 2013, Soc. Choice Welf..

[12]  José Carlos Rodriguez Alcantud,et al.  On measures of cohesiveness under dichotomous opinions: Some characterizations of approval consensus measures , 2013, Inf. Sci..

[13]  On the measurement of sociopolitical consensus in direct democracies: Proposal of indexes , 2013 .

[14]  Zeshui Xu,et al.  On Consensus of Group Decision Making with Interval Utility Values and Interval Preference Orderings , 2012, Group Decision and Negotiation.