Weighted Committee Games

Weighted committee games generalize n-player simple voting games to m ≥ 3 alternatives. The committee’s aggregation rule treats votes anonymously but parties, shareholders, members of supranational organizations, etc. differ in their numbers of votes. Infinitely many vote distributions induce only finitely many distinct mappings from preference profiles to winners, i.e., non-equivalent committees. We identify and compare all committees which use Borda, Copeland, plurality or antiplurality rule. Their geometry and differing numbers of equivalence classes – e.g., 51 for Borda vs. 4 for Copeland rule if n = m = 3 – have so far escaped notice. They determine voting equilibria, the distribution of power and other aspects of collective choice.