Arrow's Theorem

Arrow's impossibility theorem comes from a paradox in social choice theory that applies to understanding voting preference rankings by individuals and by groups. The theorem asserts that when given a choice between three or more options, any rational individual's ranking of choices in a fair election cannot be extended to reflect that of the group. As the economist Kenneth Arrow demonstrated mathematically, unless there is some precondition being met that compromises the fairness of a particular election, such as the existence of a dictator, then in a completely fair election it is impossible to guess with certainty the entire group's preference rankings based on the rankings by the individuals in the group. The real-world manifestation of Arrow's theorem is sometimes visible in elections involving public policy or a choice of three or more candidates. In elections like these, it is impossible to forecast winners with absolute certainty based on the rankings of individuals in the group, and indeed even the least popular options can still emerge victorious.

SEE ALSO Voting Behavior .


Arrow, Kenneth. Social Choice and Individual Values (1951). New Haven, CT: Yale University Press, 3rd ed., 2012.

Cory Jensen
Schenectady County Community College