[论文解读] Robustness of Approval-Based Multiwinner Voting Rules

Piotr Faliszewski, Grzegorz Gawron+1 more|arXiv (Cornell University)|Jan 27, 2026

Game Theory and Voting Systems被引用 0

一句话总结

论文分析了基于容忍度的多胜选投票规则对小投票扰动的鲁棒性，刻画了增加/移除/交换操作的鲁棒性水平，并研究鲁棒性半径问题的计算复杂度和计数变体。

ABSTRACT

We investigate how robust approval-based multiwinner voting rules are to small perturbations in the votes. In particular, we consider the extent to which a committee can change after we add/remove/swap one approval, and we consider the computational complexity of deciding how many such operations are necessary to change the set of winning committees. We also consider the counting variants of our problems, which can be interpreted as computing the probability that the result of an election changes after a given number of random perturbations of the given election.

研究动机与目标

• Motivate the study of robustness of approval-based multiwinner elections to small input perturbations.
• Define three operation-based robustness notions (Add, Remove, Swap) and the Robustness Radius problem for these rules.
• Classify robustness levels and compute complexity (polynomial-time vs NP-hard) for a range of rules.
• Investigate counting variants to determine probabilities that random perturbations change election outcomes.
• Provide a unified treatment across Thiele rules including CC, PAV, GreedyCC, GreedyPAV, and Phragmén.

提出的方法

• Formalize Op-robustness and Robustness-Radius concepts for approval-based multiwinner rules.
• Analyze seven voting rules (AV, SAV, CC, PAV, GreedyCC, GreedyPAV, Phragmén) under Add/Remove/Swap perturbations.
• Prove 1-robustness for AV across all operation types; show SAV has k-Add/k-Remove robust and 1-Swap robust; characterize unit-decreasing Thiele rules as k-robust for all operations.
• Show robustness radius results: polynomial for AV and SAV; NP-hard for CC, PAV, GreedyCC, GreedyPAV, Phragmén for most operations.
• Introduce counting variants to compute probabilities of outcome-change under random perturbations (FP for AV, #P-hard for SAV).

实验结果

研究问题

• RQ1 How robust are approval-based multiwinner rules to single-approval perturbations (Add/Remove/Swap)?
• RQ2 What is the minimum number of perturbations (Robustness Radius) needed to change the set of winning committees under each rule?
• RQ3 What is the probability that a given number of random perturbations changes the election result (counting variants)?
• RQ4 How do different rule families (AV, SAV, CC, PAV, Greedy variants, Phragmén) compare in robustness and computational complexity?
• RQ5 Do unit-decreasing Thiele rules share a common robustness property across perturbation types?

主要发现

• AV is 1-Op-Robust for Add, Remove, and Swap perturbations.
• SAV is k-Add-robust and k-Remove-robust, but 1-Swap-robust; its robustness differs between perturbation types.
• Unit-decreasing Thiele rules (including CC and PAV) are k-Op-robust for all three operation types.
• Robustness Radius decision problems are polynomial for AV and SAV, but NP-hard for CC, PAV, GreedyCC, GreedyPAV, and Phragmén (for most operation types).
• Counting variants: robustness counting is in FP for AV but #P-hard for SAV (for Add/Remove).