Old and New Monotonicity Properties

Suppose that each ballot consists of a strict preference ranking of the alternatives, that alternative x has just won the election, and that a single voter now changes her ballot by moving x higher up in the ranking (without changing her relative preference among other alternatives). The standard monotonicity property of social choice theory asserts, in any such scenario, that x should remain the winner. Loosely, then, when a change in the profile yields some change in election outcome, the two changes should not point in “opposite directions.”