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Condorcet Completion Methods that Inhibit Manipulation through Exploiting Knowledge of Electorate Preferences

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  • Richard F. Potthoff

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

Abstract

This paper attacks a problem like the one addressed in an earlier work (Potthoff, 2013) but is more mathematical. The setting is one where an election is to choose a single winner from m (> 2) candidates, it is postulated that voters have knowledge of the preference profile of the electorate, and preference cycles are limited. Both papers devise voting systems whose two key goals are to select a Condorcet winner (if one exists) and to resist manipulation. These systems entail equilibrium strategies where everyone votes sincerely, no group of voters sharing the same preference ordering can gain by deviating given that no one else deviates, and the Condorcet candidate wins. The present paper uses two unusual ballot types. One asks voters to rank the candidates with respect both to their own preferences and to their discerned order of preference of the entire electorate. The other just asks voters for their own preference ranks plus approval votes. Novel mathematical elements distinguish this paper. Its Condorcet completion methods examine all candidate triples, sometimes analyze loop(s) of some of those triples, and order candidates in a set by first determining the last-place candidate. Its non-manipulability proofs involve mathematical induction on m .

Suggested Citation

  • Richard F. Potthoff, 2014. "Condorcet Completion Methods that Inhibit Manipulation through Exploiting Knowledge of Electorate Preferences," Games, MDPI, vol. 5(4), pages 1-30, October.
    • Handle: RePEc:gam:jgames:v:5:y:2014:i:4:p:204-233:d:41815
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    References listed on IDEAS

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    1. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    2. Richard Potthoff, 2013. "Simple manipulation-resistant voting systems designed to elect Condorcet candidates and suitable for large-scale public elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 101-122, January.
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    6. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
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    Cited by:

    1. Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    2. Richard F. Potthoff, 2019. "Three Bizarre Presidential-Election Scenarios: The Perils of Simplism," Social Sciences, MDPI, vol. 8(5), pages 1-23, April.
    3. Richard Potthoff & Michael Munger, 2015. "Condorcet polling can yield serendipitous clues about voter views," Public Choice, Springer, vol. 165(1), pages 1-12, October.

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