A Weak Characterization of the Simple Majority Rule

May’s (1952) celebrated characterization of the simple majority rule appealed to four properties: decisiveness, neutrality, anonymity and positive responsiveness. The impression that they are too strong for this job was, however, extremely appealing. The aim of this paper is to present characterizations of the majority rule that appeal to properties which substantially weaken some of May’s axioms. First, I prove that we can replace positive responsiveness with a weaker version of it, and still succeed in characterizing the majority rule. Secondly, I show that we can also dispense with anonymity and neutrality, and appeal to a weaker property called binary opposition. May’s (1952) celebrated characterization of the simple majority rule appealed to four properties: decisiveness, neutrality, anonymity and positive responsiveness. The impression that they are too strong for this job was, however, quite attractive. Positive responsiveness was the main subject of the attack. Some authors believed that it is not necessary, and tried to present characterizations of the majority rule that do not make use of it (Maskin: 1995; Campbell, Kelly: 2000). Others tried to use variants of it that would be more suited to uncover the structure of the defining properties of the simple majority rule (Woeginger: 2005). Anonymity was also criticized for being too strong: this is apparent in the case of infinite electorates, since it is not able to discriminate between infinite sets (Fey: 2004). The aim of this paper is to present characterizations of the majority rule that appeal to properties which substantially weaken some of May’s axioms. The primary focus is May’s positive responsiveness property. I introduce two new responsiveness axioms and show that they help characterize the majority rule. They differ from May’s property in that they require taking into account not two profiles of a given society, but two different societies. I prove that we can replace positive responsiveness with a weaker version of it, and still succeed in characterizing the majority rule. This new responsiveness property is shortly compared with the Maskin monotonicity. Secondly, I