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The Paradox of Grading Systems

Author

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  • Brams, Steven
  • Potthoff, Richard

Abstract

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, such as approval voting, in which voters can give two grades—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.

Suggested Citation

  • Brams, Steven & Potthoff, Richard, 2015. "The Paradox of Grading Systems," MPRA Paper 63268, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:63268
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    References listed on IDEAS

    as
    1. Richard F. Potthoff, 2014. "Condorcet Completion Methods that Inhibit Manipulation through Exploiting Knowledge of Electorate Preferences," Games, MDPI, Open Access Journal, vol. 5(4), pages 1-30, October.
    2. repec:spr:stchwe:978-3-540-79128-7 is not listed on IDEAS
    3. Antoinette Baujard & Frédéric Gavrel & Herrade Igersheim & Jean-François Laslier & Isabelle Lebon, 2013. "Who's favored by Evaluative Voting? An experiment conducted during the 2012 French Presidential Election," Post-Print halshs-00950309, HAL.
    4. Steven Brams & Peter Fishburn, 2005. "Going from theory to practice: the mixed success of approval voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 457-474, December.
    5. Claude Hillinger, 2005. "The Case for Utilitarian Voting," Homo Oeconomicus, Institute of SocioEconomics, vol. 23, pages 295-321.
    6. 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.
    7. repec:cup:apsrev:v:81:y:1987:i:02:p:509-524_19 is not listed on IDEAS
    8. Michel Balinski & Rida Laraki, 2011. "Majority Judgment: Measuring, Ranking, and Electing," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015137, March.
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    Cited by:

    1. Pierre Dehez & Victor Ginsburgh, 2018. "Approval Voting and Shapley Ranking," Working Papers ECARES 2018-09, ULB -- Universite Libre de Bruxelles.

    More about this item

    Keywords

    Voting; elections; ranking system; grading system; approval voting; Condorcet paradox;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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