Influence in weighted committees

Abstract

Committee decisions on more than two alternatives much depend on the adopted aggregation rule, and so does the distribution of power among committee members. We quantify how different voting methods such as pairwise majority votes, plurality voting with or without a runoff, or Borda rule map asymmetric numbers of seats, shares, voting weights, etc. to influence on collective outcomes when individual preferences vary. Generalizations of the Penrose-Banzhaf and Shapley-Shubik power indices are proposed and applied to elections of the IMF Managing Director. Previous analysis of a priori power in binary voting is thus extended to universal social choice rules.