Multi-winner scoring election methods: Condorcet consistency and paradoxes

摘要

The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc. These four election methods are extensions of usual scoring rules designed for electing a single winner and are compared on the basis of two criteria. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability for a peculiar voting rule to select the Condorcet committee, provided that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: the Prior Successor Paradox and the Leaving Member Paradox, which occur when a member of an elected committee exits. Aside from these two extensions, this paper is one of the very rare contributions giving exact results under the Impartial Anonymous Culture (IAC) condition for the case of four candidates.