Fully Proportional Representation as Resource Allocation: Approximability Results
Abstract
We study the complexity of (approximate) winner determination under Monroe’s and ChamberlinCourant’s multiwinner voting rules, where we focus on the total (dis)satisfaction of the voters (the utilitarian case) or the (dis)satisfaction of the worstoff voter (the egalitarian case). We show good approximation algorithms for the satisfaction-based utilitarian cases, and inapproximability results for the remaining settings.