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Arrow’s Impossibility Theorem and the distinction between Voting and Deciding

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  • Colignatus, Thomas

Abstract

Arrow’s Impossibility Theorem in social choice finds different interpretations. Bordes-Tideman (1991) and Tideman (2006) suggest that collective rationality would be an illusion and that practical voting procedures do not tend to require completeness or transitivity. Colignatus (1990 and 2011) makes the distinction between voting and deciding. A voting field arises when pairwise comparisons are made without an overall winner, like in chess or basketball matches. Such (complete) comparisons can form cycles that need not be transitive. When transitivity is imposed then a decision is made who is the best. A cycle or deadlock may turn into indifference, that can be resolved by a tie-breaking rule. Since the objective behind a voting process is to determine a winner, then it is part of the very definition of collective rationality that there is completeness and transitivity, and then the voting field is extended with a decision.

Suggested Citation

  • Colignatus, Thomas, 2011. "Arrow’s Impossibility Theorem and the distinction between Voting and Deciding," MPRA Paper 34919, University Library of Munich, Germany, revised 21 Nov 2011.
    • Handle: RePEc:pra:mprapa:34919
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    File URL: https://mpra.ub.uni-muenchen.de/34919/1/MPRA_paper_34919.pdf
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    1. Colignatus, Thomas, 2011. "Response to a review of voting theory for democracy, in the light of the economic crisis and the role of mathematicians," MPRA Paper 34615, University Library of Munich, Germany, revised 09 Nov 2011.
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    Cited by:

    1. Colignatus, Thomas, 2017. "The performance of four possible rules for selecting the Prime Minister after the Dutch Parliamentary elections of March 2017," MPRA Paper 77616, University Library of Munich, Germany, revised 17 Mar 2017.

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      Keywords

      economic crisis; voting theory; democracy; economics and mathematics;
      All these keywords.

      JEL classification:

      • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
      • A10 - General Economics and Teaching - - General Economics - - - General
      • P16 - Political Economy and Comparative Economic Systems - - Capitalist Economies - - - Capitalist Institutions; Welfare State

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