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The paradox of grading systems

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  • Steven Brams
  • Richard Potthoff

Abstract

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, using two or more grades. In approval voting, voters can assign two grades only—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. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    • Handle: RePEc:kap:pubcho:v:165:y:2015:i:3:p:193-210
    DOI: 10.1007/s11127-015-0303-6
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    References listed on IDEAS

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    1. 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.
    2. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, June.
    3. Steven J. Brams & Peter C. Fishburn, 2010. "Going from Theory to Practice: The Mixed Success of Approval Voting," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 19-37, Springer.
    4. Antoinette Baujard & Herrade Igersheim & Isabelle Lebon & Frédéric Gavrel & Jean-François Laslier, 2014. "Who's favored by evaluative voting? An experiment conducted during the 2012 French presidential election," Post-Print halshs-01113068, HAL.
    5. Merrill, Samuel & Nagel, Jack, 1987. "The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules," American Political Science Review, Cambridge University Press, vol. 81(2), pages 509-524, June.
    6. Antoinette Baujard & Herrade Igersheim & Isabelle Lebon & Frédéric Gavrel & Jean-François Laslier, 2014. "Who's favored by evaluative voting? An experiment conducted during the 2012 French presidential election," PSE-Ecole d'économie de Paris (Postprint) halshs-01113068, HAL.
    7. Steven J. Brams & M. Remzi Sanver, 2009. "Voting Systems that Combine Approval and Preference," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 215-237, Springer.
    8. 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," Working Papers hal-00803024, HAL.
    9. Michel Balinski & Rida Laraki, 2011. "Majority Judgment: Measuring, Ranking, and Electing," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015137, December.
    10. Claude Hillinger, 2005. "The Case for Utilitarian Voting," Homo Oeconomicus, Institute of SocioEconomics, vol. 23, pages 295-321.
    11. 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.
    12. M. Remzi Sanver, 2010. "Approval as an Intrinsic Part of Preference," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 469-481, Springer.
    13. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, June.
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    Cited by:

    1. Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    2. Justin Kruger & M. Remzi Sanver, 2021. "An Arrovian impossibility in combining ranking and evaluation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 535-555, October.

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    More about this item

    Keywords

    Voting and elections; Grading systems; Ranking systems; Approval voting; Condorcet winner; Monte Carlo simulation;
    All these keywords.

    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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