Abstract
To choose a suitable multi-winner voting rule is a
hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice
of an “optimal” subset. In this paper, we offer a new perspective on measuring the quality of
such subsets and—consequently—of multi-winner
rules. We provide a quantitative analysis using
methods from the theory of approximation algorithms and estimate how well multi-winner rules
approximate two extreme objectives: diversity as
captured by the Approval Chamberlin–Courant rule
and individual excellence as captured by Multiwinner Approval Voting. With both theoretical and
experimental methods we classify multi-winner
rules in terms of their quantitative alignment with
these two opposing objectives