发表机构
University of Chicago（芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过偏好复形与面单调性提出拓扑条件，证明一致、匿名且面单调的社会福利函数存在时序复形连通分量可缩，并应用于固定极值域与单峰域。
AI 中文摘要
本文提供了一个拓扑构造，用于研究有限备选方案集上弱偏好的社会聚合。我们将弱偏好与类型为$A_{n-1}$的辫子排列的胞腔等同起来，并等价地，与相应的类型为$A_{n-1}$的Coxeter复形的单纯形等同起来，我们称该复形为偏好复形。然后，我们通过要求社会福利函数在作为从偏好剖面偏序集到偏好偏序集的映射时保持序关系，来定义面单调性。我们证明，如果一个共同的偏好域允许一个一致、匿名且面单调的社会福利函数，那么其序复形的几何实现的每个连通分量都是可缩的。然后我们将此构造应用于两个受限域。对于固定极值域，我们证明其序复形实现是可缩的，并利用交运算定义一个一致、匿名且面单调的社会福利函数。对于单峰域，我们证明偏好复形的相应子复形具有可缩的实现，并且在三备选方案情形下，构造一个一致、匿名且面单调的社会福利函数。
英文摘要
This paper provides a topological construction for studying social aggregation of weak preferences over a finite set of alternatives. We identify weak preferences with the cells of the type $A_{n-1}$ braid arrangement and, equivalently, with the simplices of the corresponding type $A_{n-1}$ Coxeter complex, which we call the preference complex. Then we define face-monotonicity by requiring a social welfare function to be order-preserving when viewed as a map between the preference-profile poset and the preference poset. We prove that if a common preference domain admits a unanimous, anonymous, and face-monotonic social welfare function, then every connected component of the geometric realization of its order complex is contractible. We then apply this construction to two restricted domains. For fixed-extrema domains, we prove that their order-complex realizations are contractible and define a unanimous, anonymous, and face-monotonic social welfare function using the meet operation. For single-peaked domains, we prove that the corresponding subcomplex of the preference complex has a contractible realization and, in the three-alternative case, construct a unanimous, anonymous, and face-monotonic social welfare function.
Comments24 pages, 4 figures
