Parallel axiomatizations of majority and unanimity

The relative majority rule and the unanimity rule are characterized for the case in which there are only two alternatives. The main axioms are motivated by a principle of binary representativeness: the aggregation of the preferences of n voters is the result of splitting the n voters into two groups, aggregating the preferences of the voters of each group, selecting for each group a representative that adopts the preference of the group, and finally aggregating the preferences of the two representatives. The two characterizations are shown to differ from each other in just one axiom, expressing strategyproofness (unanimity) or group strategyproofness (majority).