The result that every voting rule with at least three possible outcomes, each of which can win, is either dictatorial or open to strategic manipulation by some voter in some situation.
In more detail
Proved independently by Allan Gibbard (1973) and Mark Satterthwaite (1975). It implies that tactical voting, such as deserting a favourite candidate to stop a disliked one, cannot be designed away by any reasonable single-winner rule. Rules differ in how often and how easily they can be manipulated, and in what information a manipulator needs. Escape routes include restricting the domain of preferences (for example single-peaked preferences), allowing randomised outcomes, or using mechanisms with money.