In this paper, we use the integer programming approach to mechanism design, first introduced by Sethuraman et al. (2003), and then systematized by Vohra (2011), to reformulate issues concerning the simple majority rule. Our main result consists in showing that, when the number of agents is even, a necessary and sufficient condition for the simple majority rule to be an Arrovian social welfare function is that it is defined on a domain which is echoic with antagonistic preferences. This result is an integer programming simplified version of Theorems 2, 3, and 4 in Inada (1969).

中文翻译：

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简单多数规则和整数规划

在本文中，我们使用整数规划方法进行机制设计，首先由 Sethuraman 等人介绍。(2003)，然后由 Vohra (2011) 系统化，重新阐述有关简单多数规则的问题。我们的主要结果在于表明，当代理的数量是偶数时，简单多数规则成为 Arrovian 社会福利函数的必要和充分条件是它被定义在一个与对抗性偏好相呼应的域上。这个结果是 Inada (1969) 中定理 2、3 和 4 的整数规划简化版本。