Alternatives vs. Outcomes: A Note on the Gibbard-Satterthwaite Theorem

The Gibbard-Satterthwaite theorem is a well-known theorem from the field of social choice theory. It states that every voting scheme with at least 3 possible outcomes is dictatorial or manipulable. Later work on the Gibbard-Satterthwaite theorem frequently does not distinguish between alternatives and outcomes, thereby leading to a less general statement that requires the voting scheme to be onto. We show how the Gibbard-Satterthwaite theorem can be derived from the seemingly less general formulation