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Theorem

Arrow's Impossibility Theorem

Game Theory

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.

Facts
Statement
No 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
Proof Year
1950 1
Classification
Statement Form
Impossibility Theorem 1
Connections

Has Statement Form

In Branch

Proved By

Source Arrow's Impossibility Theorem (Wikipedia)
In the Other Atlases

Credited To

Also in Economics Atlas: credited with this subject.

Sources
1. Arrow's Impossibility Theorem (Wikipedia)
Wikimedia Foundation
  • Lead 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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