Should social choice be based on binary comparisons?

This paper argues that social choice from among more than two feasible alternatives should not be based on social choice from two‐alternative subsets. It considers in some detail the case where one alternative ties or beats every other alternative on the basis of simple majorities, and raises the question of whether such an alternative should be chosen. A condition of ‘stochastic unanimity’, introduced in this context, is shown to be incompatible with the simple majority rule when it can apply. This new condition plus a consideration of ties leads into a brief discussion of the use of individual expected utility in social choice theory.