Adrian Miroiu’s Weblog

weak_characterization_of_mj

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 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.

positive_responsiveness2

In a highly influential paper K. May characterized the simple majority rule on a finite group of voters in terms of three properties of aggregation functions: neutrality, anonymity and responsiveness. However, attempts to generalize May’s result to infinite sets of voters bring about difficulties one does not encounter in the finite case. Size is an example: all countable infinite sets are in one sense of the same ‘size’. As one may expect, size raises the question of interpreting May’s anonymity condition on infinite domains. In this context, May’s responsiveness property did not look to play a significant role. The paper argues that when the electorate is infinite, part of the import of responsiveness is that the set-theoretical Axiom of Choice holds.

Despre ce nu putem şti în mod consistent

ce_nu_putem_sti1.pdf