The Condorcet Principle for Multiwinner Elections: From Shortlisting to Proportionality

We study two notions of stability in multiwinner elections that are based on the Condorcet criterion. The first notion was introduced by Gehrlein and is majoritarian in spirit. The second one, local stability, is introduced in this paper, and focuses on voter representation. The goal of this paper is to explore these two notions, their implications on restricted domains, and the computational complexity of rules that are consistent with them.