Arrow's Impossibility Theorem
Arrow's Paradox · General Possibility Theorem
When voters have three or more distinct alternatives (options), no ranked order voting system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting a pre-specified set of criteria.
Origin
American economist Kenneth Arrow formulated the theorem in his 1951 monograph Social Choice and Individual Values (revised 1963, 2012), creating modern social choice theory. Arrow called it the "General Possibility Theorem," but it became known as Arrow's impossibility theorem. The work earned him the 1972 Nobel Prize in Economics. Arrow generalized the Marquis de Condorcet's 18th-century voting paradox, proving no ranked-choice system can satisfy independence of irrelevant alternatives while maintaining rational consistency.