Multi-Winner Elections: Justified Representation, Strategyproofness, and Risk-Avoiding Truthfulness

Abstract

We study approval-based multi-winner elections with justified representation (JR) when voters strategically report their ballots. We prove that there does not exist a strategy-proof mechanism that outputs JR committees, even when the mechanism can be randomized and only ex-ante strategy-proofness is required. The impossibility result holds for any fixed voter's monotone utility function. In addition, our impossibility result continues to hold for even more restrictive settings, such as the setting where we are allowed to select fewer than $k$ candidates, with only 4 candidates and 3 voters. Motivated by our negative results, we then ask for weaker strategy-proof guarantees under voters' partial information. We use the notion of RAT-degree proposed by Hartman, Segal-Halevi, and Tao (EC'25), the number of other voters whose information a manipulator must know before a safe and profitable deviation is possible. Standard proportional rules, such as greedy approval voting, proportional approval voting (PAV), and the method of equal shares (MES), have poor performances under the RAT-degree metric (with low RAT-degrees).