No voting rule for combining three or more ranked options into a single group ranking can simultaneously satisfy a short list of intuitively reasonable fairness conditions, unless it is a dictatorship. Proved by Kenneth Arrow, it is a foundational and pessimistic result of social choice theory.
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StatementNo voting method that turns three or more ranked options into a single group ranking can satisfy a short list of intuitively reasonable fairness conditions unless the method is a dictatorship, meaning the group ranking always matches one fixed voter's own ranking. The theorem is stated over ordinal preferences rather than intensities of preference. 1 Classification
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Source Arrow's Impossibility Theorem (Wikipedia)
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1. Arrow's Impossibility Theorem (Wikipedia)
Wikimedia FoundationLead section, statement of the theorem
It shows that no group decision-making procedure based on ordinal utilities (citizens' orderings of different alternatives) can satisfy the requirements of rational choice.
Background section, on the 1950 proof
When Kenneth Arrow proved his theorem in 1950, it inaugurated the modern field of social choice theory, a branch of welfare economics studying mechanisms to aggregate preferences and beliefs across a society.
In Group: Social Choice and Voting Theory, Lead paragraph
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow.
Proved By: Kenneth Arrow, Lead section
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow.
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