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.

翻译：多智能体系统中的一个核心问题是如何将物品公平地分配给智能体。本文首次在分配领域中对经典的多数主义社会选择函数展开分析。利用分配域的特殊结构，我们展示了一系列在一般社会选择理论中无对应结果的惊人结论。特别地，我们建立了偏好剖面与多数图之间近乎一一对应的关系。这一对应关系意味着分配的关键性质——如帕累托最优性、最小非受欢迎度与混合受欢迎度——均可仅通过关联的多数图确定。我们进一步证明所有帕累托最优分配都是半受欢迎的，且属于顶级循环。因此，通过序列独裁机制可轻易找到顶级循环中的元素。我们的主要成果是对顶级循环的完整刻画，该结果表明顶级循环仅可能由一种、两种、除两种外全部、除一种外全部或全部分配方案构成。相比之下，我们发现未被覆盖集仅包含极少数的分配方案。