在阿罗的房产上
On the Arrow property
摘要：
设X是备选方案的有限集。一个选择函数c是一个映射，它把一个S的元素c（S）赋给X的非空子集S。一个有理选择函数是这样一个函数，对于它，在备选项上存在线性排序，使得c（S）是根据该排序的S的极大元。阿罗的不可能性定理断言，在一定的自然条件下，如果至少有三个选择，那么每一个非独裁的社会选择都会产生一个非理性的选择函数。吉尔卡莱问如果阿罗的定理可以扩展到的情况下，个人的选择是不合理的，而是属于一个任意的非平凡对称类的选择函数。本文的主要定理在很一般的情况下给出了肯定的回答。
英文摘要：
Let X be a finite set of alternatives. A choice function c is a mapping which assigns to nonempty subsets S of X an element c(S) of S. A rational choice function is one for which there is a linear ordering on the alternatives such that c(S) is the maximal element of S according to that ordering. Arrow's impossibility theorem asserts that under certain natural conditions, if there are at least three alternatives then every non-dictatorial social choice gives rise to a non-rational choice function. Gil Kalai asked if Arrow's theorem can be extended to the case when the individual choices are not rational but rather belong to an arbitrary non-trivial symmetric class of choice functions. The main theorem of this paper gives an affirmative answer in a very general setting.
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。
