On measures of cohesiveness under dichotomous opinions: Some characterizations of approval consensus measures

Abstract

[EN]The measurement of the degree of agreement in a group has recently attrac- ted considerable attention by researchers from various elds. In this paper we consider situations where each member of a population classi es a list of options as either \acceptable" or \non-acceptable" (as in job committees or elections by approval voting); either \agree" or \disagree" (as in polls or surveys); either \guilty" or \not guilty" (as in jury courts); etc. In order to measure the cohesiveness that the expression of such dichotomous opinions conveys, we propose the novel concept of approval consensus measure (ACM), which does not refer to any priors of the agents like preferences or other decision-making processes. Then we give axiomatic characterizations of two generic classes of ACMs. Finally, we focus on the 2012 presidential elections in USA as a real scenario to put in practice these two proposals