单峰谷域上的防策略集合值选择
Strategy-Proof Set-Valued Choice on Single-Dipped Domains
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- Indian Statistical Institute（印度统计研究所）
- Ashoka University（阿肖卡大学）
- Shiv Nadar University（希夫·纳德大学）
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中文总结 AI 辅助
本文研究单峰谷偏好下防策略集合值选择，提出响应扩展下端点限制与匿名阈值规则，并刻画投票委员会及群体防策略性质。
中文摘要 AI 辅助
我们研究防策略的社会选择问题，其中代理具有单峰谷偏好，结果可以是备选方案的集合。虽然点值防策略规则选择一个端点，我们询问当集合通过响应扩展进行比较时哪些结果能够存续。在标准响应扩展下，对固定长度区间的偏好保持单峰谷，因此端点限制持续存在，匿名性产生单一阈值规则。在响应支配下，所有响应扩展共有的不完全序，内部区间可以存续，因为两个极端区间不必可比。对于任意集合，要求每个被选择的备选方案被某些代理最偏好，产生投票委员会规则，每个端点一个委员会；匿名规则具有双阈值配额形式。该刻画在整个端点峰谷域上成立，并且每个此类规则都是群体防策略的。
英文摘要
We study strategy-proof social choice where agents have single-dipped preferences and outcomes may be sets of alternatives. While point-valued strategy-proof rules select an endpoint, we ask which outcomes survive when sets are compared through responsive extensions. Under the standard responsive extension, preferences over fixed-length intervals remain single-dipped, so the endpoint restriction persists and anonymity yields a single-threshold rule. Under responsive dominance, the incomplete order shared by all responsive extensions, an interior interval can survive because the two extreme intervals need not be comparable. For arbitrary sets, requiring every chosen alternative to be most preferred by some agent yields voting-by-committees rules, with one committee per endpoint; anonymous rules have a two-threshold quota form. The characterization holds on the entire endpoint-peaked domain, and every such rule is group-strategy-proof.
