When are committees of Condorcet winners Condorcet winning committees?

Abstract

We consider seat-posted (or designated-seat) committee elections, where disjoint sets of candidates compete for each seat. We assume that each voter has a collection of seat-wise strict rankings of candidates, which are extended to a strict ranking of committees by means of a preference extension. We investigate conditions upon preference extensions for which seat-wise Condorcet candidates, whenever all exist, form the Condorcet winner among committees. We characterize the domain of neutral preference extensions for which the committee of seat-wise winners is the Condorcet winning committee, first assuming the latter exists (Theorem 1) and then relaxing this assumption (Theorem 2). Neutrality means that preference extensions are not sensitive to the names of candidates. Moreover, we show that these two characterizations can be stated regardless of which preference level is considered as a premise.