社会福利函数的模态逻辑（英文）

A Modal Logic for Social Welfare Functions

社会选择理论的重点是将个人偏好汇总为群体偏好的框架。我们在本文中提出了一种用于偏好聚合的模态逻辑。该逻辑是对社会福利函数的直接且易于理解的形式化。一个标准的n-ary模态框用于表征线性方案集上的n-ary函数。我们证明了社会福利功能的所有可能性质都可以用这种简单的模态语言来表达。我们为逻辑提供了一个完整的演绎系统,提供了Arrow的社会福利函数不可能定理的句法证明。

The focus of social choice theory is on frameworks of aggregating individuals’preferences into a group preference.We present in this paper a modal logic for preference aggregation.The logic is a direct and easily readable formalization of social welfare functions.A standard n-ary modal box is used to characterize n-ary functions on the set of linear orders over alternatives.We show that all possible properties of social welfare functions can be expressed by this simple modal language.We give a complete deductive system for the logic.We present a syntactic proof of Arrow’s impossibility theorem of social welfare functions.