>[!abstract] >Arrow’s impossibility theorem, formulated by economist Kenneth Arrow, demonstrates that no voting system can perfectly translate individual preferences into a collective decision while satisfying a set of fairness criteria. Specifically, when there are three or more options, no rank-order voting method can simultaneously meet unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. > >The theorem reveals fundamental limits in social choice: any voting rule must sacrifice at least one intuitive notion of fairness or consistency. It has profound implications for political theory, economics, and decision-making, showing that collective choice is inherently constrained by structural trade-offs. > >A dictatorship rule (one person'’'s preferences determine the outcome) technically satisfies Arrow’s conditions but destroys fairness. >[!related] >- **North** (upstream): [[Intransitivity]] >- **West** (similar): [[Condorcet paradox]] >- **East** (different): [[Transitivity]] >- **South** (downstream): [[Gibbard–Satterthwaite theorem]]