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

Year: 2026
Type: preprint
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 strategyproofness is required. The impossibility already holds with three voters, four candidates, and target committee size three, even when the mechanism may select fewer than three candidates. It applies to every common strictly increasing cardinality-based utility function and scales to every target size $k\geq3$, every number of voters divisible by $k$, and every candidate-set size at least $k+1$. Motivated by our negative results, we then ask for weaker strategy-proof guarantees under voters' partial information. We use the notion of Risk-Avoiding Truthfulness and its 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, and the Method of Equal Shares, have poor performances under the RAT-Degree metric (with low RAT-Degrees). Finally, for $n$ voters, we construct a JR mechanism with RAT-Degree at least $n-5$, without a polynomial-time bound. We then use the same idea together with algebraic ballot encodings to obtain a polynomial-time JR mechanism with RAT-Degree at least $n-7$. When voters also have immutable private identifiers and both the identifiers and ballots of unknown voters are unobserved, we obtain a polynomial-time JR mechanism with RAT-Degree at least $n-1$ for $2\le k
DOI: 10.48550/arxiv.2608.15370
Open Access status: green
OpenAlex ID: W7203679650
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