Nondictatorial Arrovian social welfare functions, simple majority rule, and integer programming.

In this paper, we use the linear programming approach to mechanism design, first introduced by Sethuraman et al. (2003) and then systematized by Vohra (2011), to analyze nondictatorial Arrovian social welfare functions with and without ties. First, we provide a new and simpler proof of Theorem 2 in Kalai and Muller (1977), which characterizes the domains admitting nondictatorial Arrovian social welfare functions without ties. Then, we show that a domain containing an inseparable ordered pair admits nondictatorial Arrovian social welfare functions with ties, thereby strengthening a result previously obtained by Kalai and Ritz (1978). Finally, we propose a reformulation of the simple majority rule in the framework of integer programming with an odd or even number of agents. We use this reformulation to recast some celebrated theorems, proved by Arrow (1963), Sen (1966), and Inada (1969), which provide conditions guaranteeing that the simple majority rule is a nondictatorial Arrovian social welfare function