Minimal Manipulability: Anonymity and Surjectivity

Gibbard''s (1973) and Satterthwaite''s (1975) result implies that anonymous surjective social choice functions on more than two alternatives are manipulable. Placing some mild constraints on the number of agents compared to the number of alternatives, we show what the minimal number of manipulable profiles of such social choice functions is. Moreover, all such social choice functions attaining the lower bound are characterized. They show a trade off between minimizing manipulability and treating alternatives neutrally.