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Minimal voting paradoxes

Author

Listed:
  • Felix Brandt

    (9184Technische Universität München, Germany)

  • Marie Matthäus

    (Technische Universität München, Germany)

  • Christian Saile

    (Technische Universität München, Germany)

Abstract

Voting paradoxes date back to the origin of social choice theory in the 18th century, when the Chevalier de Borda pointed out that plurality—then and now the most common voting rule—may elect a candidate who loses pairwise majority comparisons against every other candidate. Since then, a large number of similar, seemingly paradoxical, phenomena have been observed in the literature. As it turns out, many paradoxes only materialize under some rather contrived circumstances and require a certain number of voters and candidates. In this paper, we leverage computational optimization techniques to identify the minimal numbers of voters and candidates that are required for the most common voting paradoxes to materialize. The resulting compilation of voting paradoxes may serve as a useful reference to social choice theorists as well as an argument for the deployment of certain rules when the numbers of voters or candidates are severely restricted.

Suggested Citation

  • Felix Brandt & Marie Matthäus & Christian Saile, 2022. "Minimal voting paradoxes," Journal of Theoretical Politics, , vol. 34(4), pages 527-551, October.
    • Handle: RePEc:sae:jothpo:v:34:y:2022:i:4:p:527-551
    DOI: 10.1177/09516298221122104
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    References listed on IDEAS

    as
    1. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
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    3. Dominique Lepelley & Hatem Smaoui, 2019. "Comparing Two Ways for Eliminating Candidates in Three-Alternative Elections Using Sequential Scoring Rules," Group Decision and Negotiation, Springer, vol. 28(4), pages 787-804, August.
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    5. Dan S. Felsenthal & Hannu Nurmi, 2019. "The No-Show Paradox Under a Restricted Domain," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(4), pages 277-293, April.
    6. William V. Gehrlein, 2006. "Condorcet’s Paradox," Theory and Decision Library C, Springer, number 978-3-540-33799-7, December.
    7. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
    8. Gehrlein, William V. & Fishburn, Peter C., 1978. "Probabilities of election outcomes for large electorates," Journal of Economic Theory, Elsevier, vol. 19(1), pages 38-49, October.
    9. Felix Brandt & Maria Chudnovsky & Ilhee Kim & Gaku Liu & Sergey Norin & Alex Scott & Paul Seymour & Stephan Thomassé, 2013. "A counterexample to a conjecture of Schwartz," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 739-743, March.
    10. Florian Brandl & Felix Brandt, 2020. "Arrovian Aggregation of Convex Preferences," Econometrica, Econometric Society, vol. 88(2), pages 799-844, March.
    11. Brandt, Felix & Geist, Christian & Peters, Dominik, 2017. "Optimal bounds for the no-show paradox via SAT solving," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 18-27.
    12. Dan S. Felsenthal & Hannu Nurmi, 2019. "Voting Procedures Under a Restricted Domain," SpringerBriefs in Economics, Springer, number 978-3-030-12627-8, January.
    13. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    14. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2018. "On the structure of stable tournament solutions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 483-507, March.
    15. Florian Brandl & Felix Brandt & Hans Georg Seedig, 2016. "Consistent Probabilistic Social Choice," Econometrica, Econometric Society, vol. 84, pages 1839-1880, September.
    16. Hannu Nurmi, 2020. "The Incidence of Some Voting Paradoxes Under Domain Restrictions," Group Decision and Negotiation, Springer, vol. 29(6), pages 1107-1120, December.
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    Cited by:

    1. Barbaro Salvatore, 2025. "Wie sollten wir unseren Bundestag wählen?," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 26(4), pages 472-480.
    2. Brandt, Felix & Dong, Chris & Peters, Dominik, 2025. "Condorcet-consistent choice among three candidates," Games and Economic Behavior, Elsevier, vol. 153(C), pages 113-130.

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