Egalitarian committee scoring rules

Abstract

We introduce and study the class of egalitarian variants of committee scoring rules, where instead of summing up the scores that voters assign to committees-as is done in the utilitarian variants-the score of a committee is taken to be the lowest score assigned to it by any voter. We focus on five rules, which are egalitarian analogues of SNTV, the k-Borda rule, the Chamberlin-Courant rule, the Bloc rule, and the Pessimist rule. We establish their computational complexity, provide their initial axiomatic study, and perform experiments to represent the action of these rules graphically.