Abstract During the 20th century, impossibility theorems have become an important part of mathematics. Arrow's impossibility theorem (1950) stands out as one of the first impossibility theorems outside of pure mathematics. It states that it is impossible to design a welfare function (or a voting method) that satisfies some rather innocent looking requirements. Arrow's theorem became the starting point of social choice theory that has had a great impact on welfare economics. This paper will analyze the history of Arrow's impossibility theorem in its mathematical and economic contexts. It will be argued that Arrow made a radical change of the mathematical model of welfare economics by connecting it to the theory of voting and that this change was preconditioned by his deep knowledge of the modern axiomatic approach to mathematics and logic.

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数学不可能性如何改变福利经济学：阿罗不可能性定理的历史

摘要 20世纪，不可能定理成为数学的重要组成部分。阿罗不可能性定理 (1950) 是纯数学之外的第一个不可能性定理之一。它指出不可能设计出满足一些看起来很无辜的要求的福利函数（或投票方法）。阿罗定理成为对福利经济学产生重大影响的社会选择理论的起点。本文将分析阿罗不可能定理在其数学和经济背景下的历史。