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Control of Condorcet voting: Complexity and a Relation-Algebraic approach

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  • Berghammer, Rudolf
  • Schnoor, Henning

Abstract

We study the constructive variant of the control problem for Condorcet voting, where control is done by deleting voters. We prove that this problem remains NP-hard if instead of Condorcet winners the alternatives in the uncovered set win. Furthermore, we present a relation-algebraic model of Condorcet voting and relation-algebraic specifications of the dominance relation and the solutions of the control problem. All our relation-algebraic specifications immediately can be translated into the programming language of the OBDD-based computer system RelView. Our approach is very flexible and especially appropriate for prototyping and experimentation, and as such very instructive for educational purposes. It can easily be applied to other voting rules and control problems.

Suggested Citation

  • Berghammer, Rudolf & Schnoor, Henning, 2015. "Control of Condorcet voting: Complexity and a Relation-Algebraic approach," European Journal of Operational Research, Elsevier, vol. 246(2), pages 505-516.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:2:p:505-516
    DOI: 10.1016/j.ejor.2015.04.025
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    References listed on IDEAS

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    1. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2013. "Computing tournament solutions using relation algebra and RelView," European Journal of Operational Research, Elsevier, vol. 226(3), pages 636-645.
    2. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
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    4. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    5. John Duggan, 2011. "Uncovered Sets," Wallis Working Papers WP63, University of Rochester - Wallis Institute of Political Economy.
    6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    7. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
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