Oligarchic majority rules bring the voice but no vote principle into effect. We prove characterizations of the oligarchic majority rules both for fixed and unrestricted societies and a binary agenda. This is a general class of rules that includes the simple majority rule as well as dictatorships. Suitable sets of axioms identify a (possibly empty) subsociety whose members have voice but no vote, and valid votes are aggregated by the majority rule. Relatedly, we also prove an alternative characterization of the majority rule for unrestricted societies and a binary agenda. It uses neither of the three original axioms from the characterization by May [Econometrica 20 (1952) 680] for fixed societies that confront two alternatives.
