Construct · 1 fields · 3 citations

Arrow's impossibility theorem: a standalone construct

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Arrow'simpossibility theorem1 CONSTRUCTArrow's theoremARROW · VOTING PARADOX

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Social choice theory

The proof that no fair rank-order voting rule can aggregate individual preferences into a single group ranking

Kenneth Arrow's 1950 paper A difficulty in the concept of social welfare, expanded in his 1951 book Social choice and individual values, proved that no rank-order voting rule can turn the ranked preferences of a group of individuals into a single community-wide ranking while meeting a short list of reasonable fairness conditions at the same time. Those conditions are unrestricted domain (the rule must accept any set of individual rankings), the Pareto principle (if everyone prefers one option to another, the group ranking must agree), independence of irrelevant alternatives (the group's ranking of any two options depends only on how individuals rank those two, not on a third option), and non-dictatorship (no single person's ranking always decides the outcome). Arrow showed that when there are three or more options, the only rule that satisfies the first three conditions is a dictatorship, so all four conditions cannot hold together. He stated the conditions as formal axioms and derived the result as a mathematical proof, an approach that founded the modern field of social choice theory and reframed welfare economics and voting theory around what preference-aggregation rules can and cannot achieve.[1][2][3]

Unit
A formal impossibility result: a proof that a stated set of fairness axioms for preference aggregation cannot be jointly satisfied
Recovery means
Not applicable
Measured by
Established by mathematical proof from the stated axioms; a given voting rule is assessed by checking which of the four conditions it must violate

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Nearby constructs

welfare4 fields · 4 citationsjingle · one word, four constructspreference4 fields · 7 citationsjingle · one word, four constructsbook1 fields · 1 citationsanchor · a standalone construct

References

  1. Arrow, K. J. (1950). A difficulty in the concept of social welfare. Journal of Political Economy, 58(4), 328-346. https://doi.org/10.1086/256963
  2. Arrow, K. J. (1951). Social choice and individual values. Wiley.
  3. Sen, A. (1999). The possibility of social choice. The American Economic Review, 89(3), 349-378. https://doi.org/10.1257/aer.89.3.349

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