单峰与单谷偏好域上的匿名性与防策略性
Anonymity and strategy-proofness on a domain of single-peaked and single-dipped preferences
AI总结：
研究了智能体具有单峰或单谷偏好时公共设施定位问题，刻画了该域上所有防策略且类型匿名的规则，提出基于中位数与双重配额多数方法的两步选择机制，并证明其与现有刻画的等价性。
摘要：
我们分析了在智能体具有单峰或单谷偏好的社会中，于直线上定位公共设施的问题。我们考虑了 Alcalde-Unzu et al. (2024) 分析的偏好域，其中每个智能体的偏好类型是公开信息，但其峰/谷的位置以及偏好的其余部分是未知的。我们刻画了该偏好域上所有防策略且类型匿名的规则。基于现有结果，我们提供了一个两步刻画：首先，计算峰值与一组固定值之间的中位数（Moulin, 1980），得到单个备选项或一对相邻备选项。如果中位数的结果是一对，我们在第二步应用“双重配额多数方法”在该对中的两个备选项之间进行选择（Moulin, 1983）。我们还展示了类型匿名性对 Alcalde-Unzu et al. (2024) 所刻画的防策略规则施加的额外条件。最后，我们证明了这两种刻画之间的等价性。
英文摘要：
We analyze the problem of locating a public facility on a line in a society where agents have either single-peaked or single-dipped preferences. We consider the domain analyzed in Alcalde-Unzu et al. (2024), where the type of preference of each agent is public information, but the location of her peak/dip as well as the rest of the preference are unknown. We characterize all strategy-proof and type-anonymous rules on this domain. Building on existing results, we provide a two-step characterization": first, the median between the peaks and a collection of fixed values is computed (Moulin, 1980), resulting in either a single alternative or a pair of contiguous alternatives. If the outcome of the median is a pair, we apply a double-quota majority method" in the second step to choose between the two alternatives in the pair (Moulin, 1983). We also show the additional conditions that type-anonymity imposes on the strategy-proof rules characterized by Alcalde-Unzu et al. (2024). Finally, we show the equivalence between the two characterizations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
