Abstract
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).
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