风险规避委员会选择的防策略性程度

中文摘要 AI 辅助

经典的防策略性概念隐含假设操纵者要么完全知晓其他所有参与者的报告，要么愿意冒险行事。为捕捉现实世界选民的深度不确定性，近期工作引入了风险规避真实性（RAT）和RAT程度，后者量化了操纵严格安全所需已知报告的确切数量。虽然RAT程度已在单胜者选举等场景中分析，但其对多胜者投票的影响尚未探索。本文通过将RAT程度框架扩展到基于批准的委员会（ABC）选择来弥合这一差距，聚焦突出的比例批准投票（PAV）规则，研究其对安全子集操纵的敏感性。我们在候选人减少的情况下建立了其超集风险规避防策略性的紧密界限，表明当操纵者知晓$f = \lceil n/k \rceil$个其他选民的确切选票时，PAV易受安全操纵，但在最多知晓$f = \lfloor \frac{n}{k + 1} \rfloor - 1$个选民时则完全免疫。

英文摘要

Classical strategyproofness assumes a manipulator either knows how everyone else votes or is willing to gamble as if they did. Real voters rarely do. The recently introduced RAT-degree measures how many other participants' reports an agent must actually observe before a manipulation becomes strictly safe, interpolating between full truthfulness and immunity to blind manipulation. While previously explored in auctions and single-winner settings, we bring this measure to multi-winner elections. We apply it to Approval-Based Committee (ABC) rules under free-riding: a voter drops approved candidates from their truthful ballot to concentrate weight on marginal ones. We first analyze Proportional Approval Voting (PAV). Knowledge of $\lceil n/k \rceil$ ballots already enables a safe and strictly profitable drop, whereas knowledge of at most $\lfloor n/(k+1) \rfloor - 1$ ballots leaves the rule completely immune; an explicit instance shows the latter bound cannot be raised in general. Since a manipulator informed about roughly a $1/k$ fraction of the electorate therefore suffices, we ask how much proportionality must be surrendered to buy strategic robustness. We introduce $d$-RPAV, a parameterized family of Thiele rules with weights $d/(j+d-1)$ that recovers PAV at $d = 1$ and approaches Approval Voting (AV) as $d$ grows. We prove that $d$-RPAV satisfies $α$-Justified Representation ($α$-JR) for $α= d$, and is immune to safe free-riding given up to $\lfloor dn/(k+2d-1) \rfloor - 1$ known ballots, yielding a clean and tunable trade-off between proportional representation and strategic robustness.

发表机构

• The Open University of Israel（以色列开放大学）

机构由 AI 辅助整理，请以论文原文为准。