Glossary term
Arrow's impossibility theorem
Also: Arrow's paradox, general possibility theoremЧитать на русском
Kenneth Arrow's result that, with three or more options, no rule turning individual rankings into a group ranking can satisfy a short list of fairness conditions at once without making someone a dictator.
In more detail
The conditions are unrestricted domain, weak Pareto, independence of irrelevant alternatives and non-dictatorship. The theorem concerns rank-order aggregation. Rules that use richer information, such as scores or approvals, or that restrict preferences, for example single-peaked ones, change the assumptions. It is often misread as 'no voting system is fair'; it says only that these specific conditions cannot all hold.