Majority rule as a unique voting method in elections with multiple candidates

May's classical theorem states that in a single-winner choose-one voting system with just two candidates, majority rule is the only social choice function satisfying anonimity, neutrality and positive responsiveness axiom. Anonimity and neutrality are usually regarded as very natural constraints on the social choice function. Positive responsiveness, on the other hand, is sometimes deemed too strong of an axiom, which stimulates further search for less stringent conditions. One viable substitute is Gerhard J. Woeginger's "reducibility to subsocieties". We demonstrate that the condition generalizes to more than two candidates and, consequently, characterizes majority rule for elections with multiple candidates.