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Radial Symmetry Does Not Preclude Condorcet Cycles If Different Voters Weight the Issues Differently

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  • Richard F. Potthoff

    (Department of Political Science and Social Science Research Institute, Duke University, Box 90420, Durham, NC 27708, USA)

Abstract

Radial symmetry, by our definition, is a precise condition on continuous ideal-point distributions, rarely if ever found exactly in practice, that is similar to the classical 1967 symmetry condition of Plott but pertains to an infinite electorate; the bivariate normal distribution provides an example. A Condorcet cycle exists if the electorate prefers alternative X to Y , Y to Z , and Z to X . An alternative K is a Condorcet winner if there is no alternative that the electorate prefers to K . Lack of a Condorcet winner may engender turmoil. The nonexistence of a Condorcet winner implies that a Condorcet cycle exists. Radial symmetry precludes the existence of Condorcet cycles and thus guarantees a Condorcet winner; but this result assumes that all voters weight the dimensions alike. Our counterexamples show that a Condorcet cycle can arise, even under radial symmetry, if the weighting of issues varies across voters. This finding may be of more than theoretical value: It may suggest that in an empirical setting (without radial symmetry), a Condorcet cycle may be more frequent if voters differ as to how they weight the dimensions. We examine, for illustration based on two dimensions (left–right, linguistic), a Condorcet preference cycle in Finland’s 1931 presidential election.

Suggested Citation

  • Richard F. Potthoff, 2022. "Radial Symmetry Does Not Preclude Condorcet Cycles If Different Voters Weight the Issues Differently," Economies, MDPI, vol. 10(7), pages 1-17, July.
  • Handle: RePEc:gam:jecomi:v:10:y:2022:i:7:p:166-:d:861448
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    References listed on IDEAS

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    1. Paul B. Simpson, 1969. "On Defining Areas of Voter Choice: Professor Tullock on Stable Voting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 83(3), pages 478-490.
    2. Adrian Deemen, 2014. "On the empirical relevance of Condorcet’s paradox," Public Choice, Springer, vol. 158(3), pages 311-330, March.
    3. Erikson, Robert S. & Romero, David W., 1990. "Candidate Equilibrium and the Behavioral Model of the Vote," American Political Science Review, Cambridge University Press, vol. 84(4), pages 1103-1126, December.
    4. Donald G. Saari, 1997. "The generic existence of a core for q -rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 219-260.
    5. Eerik Lagerspetz, 2016. "Social Choice and Democratic Values," Studies in Choice and Welfare, Springer, edition 1, number 978-3-319-23261-4, June.
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