Popular Committees

Abstract

The computational complexity status for a problem of deciding on the quality of a committee is established. Starting with individual preferences over alternatives, we analyze when it can be determined efficiently if a given committee C satisfies a weak Condorcet criterion - i.e., if C is at least as good as every other committee in a pairwise majority comparison. Scoring functions used in classic voting rules are adapted for these comparisons. In particular, we draw the sharp separation line between computationally tractable and intractable instances with respect to different voting rules.