Axioms of monotonicity, efficiency and continuity are shown to characterize the relative majority rule when there are only two alternatives. The absolute majority rule and the relative majority rule in which indifferences are resolved following some given tie-breaking rule are also characterized using those axioms. The strategy followed in these two characterizations consists of: (i) identifying a domain D where the relative majority rule coincides with the characterized rule; and (ii) making the value of elements not in D coincide with the value of some element in D.