>[!abstract] >The Gibbard–Satterthwaite theorem is a result in social choice theory showing that, for any voting system with three or more options, if the system is deterministic and always produces a single winner, then it must be either dictatorial (one voter always determines the outcome) or vulnerable to strategic manipulation (voters can benefit from misrepresenting preferences). > >Proven independently by Allan Gibbard and Mark Satterthwaite in the 1970s, the theorem formalizes the inevitability of "tactical voting" in fair-seeming systems. It highlights intrinsic limits on designing strategy-proof, non-dictatorial voting mechanisms, influencing research in political science, economics, and mechanism design. >[!related] >- **North** (upstream): — >- **West** (similar): [[Arrow’s impossibility theorem]], [[Condorcet paradox]] >- **East** (different): — >- **South** (downstream): [[Tactical voting]]