Condorcet consistent scoring rules and single-peakedness

Abstract

We study voting problems with an odd number of agents and single-peaked preferences. With only three alternatives, there are scoring rules that yield the Condorcet winner only for committees of three and five agents. With four or more alternatives, only committees of three agents work. In all these scoring rules, the best and worst alternatives are assigned a score of 1and 0, respectively, and any middle alternative a score between 0 and 1/2 . For five or more alternatives, the score of any middle alternative must be the same, and we call this family semiplurality scoring rules.