Definition
Gibbard–Satterthwaite (1973, 1975)
Let
contain at least three alternatives and let be the number of voters. Every deterministic single-winner voting rule defined on all profiles of complete, strict preference rankings satisfies
Thus no such rule can be simultaneously surjective, non-dictatorial and non-manipulable. Single-winner output supplies resoluteness; non-manipulability is also called strategy-proofness. The unrestricted ranking domain and the requirement
are essential assumptions.