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Interpreting Arrow’s Impossibility Theorem

Author

Listed:
  • Dan Usher

    (Department of Economics, Queen's University)

Abstract
Arrow’s Impossibility Theorem is commonly understood to invoke a dictatorship that is somehow lurking within our voting arrangements. The theorem has been described as proving that “any constitution that respects transitivity, independence of irrelevant alternatives and unanimity is a dictatorship”. But the theorem is really not about dictatorship. It is more appropriately understood as being about the spoiler problem, about the possibility that the presence of a candidate who cannot win the election himself may, nevertheless, violate the “independence of irrelevant alternatives” by switching the outcome of the election between two other candidates. The theorem becomes that no electoral system is guaranteed to avoid the spoiler problem altogether, regardless of the options and regardless of voter preferences.

Suggested Citation

  • Dan Usher, 2017. "Interpreting Arrow’s Impossibility Theorem," Working Paper 1384, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1384
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1384.pdf
    File Function: First version 2017
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    More about this item

    Keywords

    Impossibility Theorem; Spoilers; Dictatorship;
    All these keywords.

    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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