The acclamation consensus state and an associated ranking rule

Abstract

The study of conditions, under which the existence of an “absolute” best winner can be assured, is a hot topic in the field of social choice. Unanimity is an evident example of a condition under which the winner is obvious. However, many more properties weaker than unanimity have been analysed in literature: the presence of a Condorcet winner, strong stochastic transitivity, the presence of a candidate that Borda dominates all other candidates, etc. Unfortunately, one could easily find a prominent ranking rule, for which the outcome does not agree with these relaxed conditions. In this study, we aim to identify a condition weaker than unanimity, but under which the social outcome is still obvious. This condition, defined as the conjunction of three properties already studied by the present authors and hereinafter referred to as acclamation, will be proven to be a meeting point for the most prominent ranking rules in social choice theory, and will be used for introducing an intuitively appealing ranking rule.