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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. 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.
    2. 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.
    3. Campbell, Donald E. & Kelly, Jerry S., 2010. "Strategy-proofness and weighted voting," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 15-23, July.
    4. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    5. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
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