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

The measurement of the degree of agreement in a group has recently attracted considerable attention by researchers from various fields. In this paper we consider situations where each member of a population classifies 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.