A Simple Characterization of Qualified Majority Voting Rules

Abstract: This note characterizes every qualified majority voting rule with a quota $q$ strictly greater than half of the voter set in environments with just two alternatives through anonymity, responsiveness, and $q$-neutrality. Crucially, the latter imposes independence of the labels of the alternatives only for all preference profiles in which some alternative is strictly top-ranked by at least $q$ voters. Thus, this note generalizes May's (1952, Theorem, p.~682) well-known axiomatic characterization of the simple majority voting rule to qualified majority voting rules with a quota $q$ strictly greater than half of the voter set. In doing so, it shows that these qualified majority voting rules are precisely distinguished by their "degree" of neutrality.