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Optimal bounds for the no-show paradox via SAT solving

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  • Brandt, Felix
  • Geist, Christian
  • Peters, Dominik

Abstract

One of the most important desirable properties in social choice theory is Condorcet-consistency, which requires that a voting rule should return an alternative that is preferred to any other alternative by some majority of voters. Another desirable property is participation, which requires that no voter should be worse off by joining an electorate. A seminal result by Moulin (1988) has shown that Condorcet-consistency and participation are incompatible whenever there are at least 4 alternatives and 25 voters. We leverage SAT solving to obtain an elegant human-readable proof of Moulin’s result that requires only 12 voters. Moreover, the SAT solver is able to construct a Condorcet-consistent voting rule that satisfies participation as well as a number of other desirable properties for up to 11 voters, proving the optimality of the above bound. We also obtain tight results for set-valued and probabilistic voting rules, which complement and significantly improve existing theorems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:90:y:2017:i:c:p:18-27
    DOI: 10.1016/j.mathsocsci.2016.09.003
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    References listed on IDEAS

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    1. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    2. Joaqui´n Pérez, 2001. "The Strong No Show Paradoxes are a common flaw in Condorcet voting correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 601-616.
    3. Felix Brandt, 2015. "Set-monotonicity implies Kelly-strategyproofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 793-804, December.
    4. Campbell, Donald E. & Graver, Jack & Kelly, Jerry S., 2012. "There are more strategy-proof procedures than you think," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 263-265.
    5. José Jimeno & Joaquín Pérez & Estefanía García, 2009. "An extension of the Moulin No Show Paradox for voting correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 343-359, September.
    6. Dominique Lepelley & Vincent Merlin, 2001. "Scoring run-off paradoxes for variable electorates," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 53-80.
    7. Campbell, Donald E. & Kelly, Jerry S., 2010. "Strategy-proofness and weighted voting," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 15-23, July.
    8. Ray, Depankar, 1986. "On the practical possibility of a `no show paradox' under the single transferable vote," Mathematical Social Sciences, Elsevier, vol. 11(2), pages 183-189, April.
    9. M. Sanver & William Zwicker, 2009. "One-way monotonicity as a form of strategy-proofness," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 553-574, November.
    10. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
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    Cited by:

    1. Leonardo Matone & Ben Abramowitz & Nicholas Mattei & Avinash Balakrishnan, 2024. "DeepVoting: Learning Voting Rules with Tailored Embeddings," Papers 2408.13630, arXiv.org.
    2. Brandt, Felix & Saile, Christian & Stricker, Christian, 2022. "Strategyproof social choice when preferences and outcomes may contain ties," Journal of Economic Theory, Elsevier, vol. 202(C).
    3. Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).
    4. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
    5. Hannu Nurmi, 2020. "The Incidence of Some Voting Paradoxes Under Domain Restrictions," Group Decision and Negotiation, Springer, vol. 29(6), pages 1107-1120, December.
    6. Martin Bullinger & Chris Dong & Patrick Lederer & Clara Mehler, 2023. "Participation Incentives in Approval-Based Committee Elections," Papers 2312.08798, arXiv.org.
    7. Brandt, Felix & Lederer, Patrick & Suksompong, Warut, 2023. "Incentives in social decision schemes with pairwise comparison preferences," Games and Economic Behavior, Elsevier, vol. 142(C), pages 266-291.
    8. 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.
    9. Wesley H. Holliday & Chase Norman & Eric Pacuit & Saam Zahedian, 2022. "Impossibility theorems involving weakenings of expansion consistency and resoluteness in voting," Papers 2208.06907, arXiv.org, revised Mar 2023.
    10. Eric Kamwa & Vincent Merlin & Faty Mbaye Top, 2023. "Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate," Working Papers hal-03143741, HAL.

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