多数派分配规则
Majoritarian Assignment Rules
AI总结：
本文研究了多智能体系统中对象公平分配问题，通过分析经典多数派社会选择函数在分配领域的特性，发现偏好配置与多数派图之间存在近似一一对应关系，从而揭示了帕累托最优、最小不受欢迎和混合受欢迎等属性可通过多数派图确定，并进一步证明了所有帕累托最优分配都属于顶级循环，且顶级循环可通过串行独裁制轻易找到。
摘要：
多智能体系统中的核心问题是在代理之间公平分配物品。在本文中，我们开始分析经典多数派社会选择函数在分配领域的分析。利用分配领域的特殊结构，我们展示了一系列在一般社会选择中没有对应结果的令人惊讶的结果。特别是，我们建立了偏好配置与多数派图之间的近似一一对应关系。这种对应关系意味着分配的关键属性--如帕累托最优、最小不受欢迎和混合受欢迎--可以仅通过关联的多数派图确定。我们进一步证明，所有帕累托最优分配都是半受欢迎的，并且属于顶级循环。顶级循环中的元素因此可以通过串行独裁制轻易找到。我们的主要结果是对顶级循环的完全表征，这表明顶级循环只能由一个、两个、除了两个之外的所有、除了一个之外的所有或所有分配组成。相比之下，我们发现未覆盖集只包含非常少的分配。
英文摘要：
A central problem in multiagent systems is the fair assignment of objects to agents. In this paper, we initiate the analysis of classic majoritarian social choice functions in assignment. Exploiting the special structure of the assignment domain, we show a number of surprising results with no counterparts in general social choice. In particular, we establish a near one-to-one correspondence between preference profiles and majority graphs. This correspondence implies that key properties of assignments -- such as Pareto-optimality, least unpopularity, and mixed popularity -- can be determined solely by the associated majority graph. We further show that all Pareto-optimal assignments are semi-popular and belong to the top cycle. Elements of the top cycle can thus easily be found via serial dictatorships. Our main result is a complete characterization of the top cycle, which implies the top cycle can only consist of one, two, all but two, all but one, or all assignments. By contrast, we find that the uncovered set contains only very few assignments.
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。
