  May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes
majority voting on two alternatives as the unique preferential voting method
satisfying several simple axioms. Here we show that by adding some desirable
axioms to May's axioms, we can uniquely determine how to vote on three
alternatives (setting aside tiebreaking). In particular, we add two axioms
stating that the voting method should mitigate spoiler effects and avoid the
so-called strong no show paradox. We prove a theorem stating that any
preferential voting method satisfying our enlarged set of axioms, which
includes some weak homogeneity and preservation axioms, must choose from among
the Minimax winners in all three-alternative elections. When applied to more
than three alternatives, our axioms also distinguish Minimax from other known
voting methods that coincide with or refine Minimax for three alternatives.
