Consensus and the Act of Voting

Abstract

In this article we are concerned with assessing the cohesiveness of a society whose individual preferences are known. We analyse the axiomatic properties of a general proposal to measure aggregate satisfaction in terms of coherence of the expressed opinions, that relies on the consensus with reference to a select social preference. The formal concept of referenced consensus measures that we introduce permits to produce a numerical social evaluation from purely ordinal individual information. A referenced consensus measure can be specialized via two ways: the specification of the representative agent, or from a practical point of view, the choice of a voting mechanism; and the measure of agreement between profiles of orderings and individual orderings. Introducing a fictitious agent, or the result of the act of voting, as a reference is fit for the common case of actual social choices. We carry out a descriptive analysis of the formal properties of referenced consensus measures with an emphasis on two relevant cases whose explicit constructions are detailed.