Kenneth May's 1952 result that, for choices between two options, simple majority rule is the only rule that is decisive, anonymous, neutral and positively responsive.
In more detail
Decisive means the rule always gives an answer (win or tie). Anonymous means swapping voters' ballots does not change the result. Neutral means relabelling the options does not favour either. Positively responsive means that if the outcome is a tie or a win for A and one voter shifts towards A, A then wins outright. The theorem is the standard formal justification for majority rule in yes/no decisions such as referendums. It does not extend to three or more options, where Arrow's theorem and the Condorcet paradox show that no rule satisfies all appealing criteria.