# Gibbard-Satterthwaite theorem

The **Gibbard-Satterthwaite theorem** states that every unimposing voting system (one in which every preference order is achievable) which chooses between three or more candidates, must be either dictatorial or manipulable (i.e. susceptible to tactical voting). It is derived from Arrow's impossibility theorem and Gibbard's theorem.

## Statement

For every voting rule, one of the following three things must hold:

- The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner
- The rule limits the possible outcomes to only two alternatives
- The rule is susceptible to strategic voting: some voter's sincere ballot may not defend their opinion best.

## Further Reading

Portions derived from "Gibbard–Satterthwaite theorem" revision 13601023. |