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Grading Exams: 100, 99, 98,...or A, B, C?

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Abstract

We introduce grading into games of status. Each player chooses effort, pro­ducing a stochastic output or score. Utilities depend on the ranking of all the scores. By clustering scores into grades, the ranking is coarsened, and the incen­tives to work are changed. We apply games of status to grading exams. Our main conclusion is that if students care primarily about their status (relative rank) in class, they are often best motivated to work not by revealing their exact numerical exam scores (100, 99, ...,1), but instead by clumping them into coarse categories (A,B,C). When student abilities are disparate, the optimal absolute grading scheme is always coarse. Furthermore, it awards fewer A’s than there are alpha-quality students, creating small elites. When students are homogeneous, we characterize optimal absolute grading schemes in terms of the stochastic dominance between student performances (when they shirk or work) on subintervals of scores, show­ing again why coarse grading may be advantageous. In both the disparate case and the homogeneous case, we prove that ab­solute grading is better than grading on a curve, provided student scores are independent.

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  • Pradeep Dubey & John Geanakoplos, 2009. "Grading Exams: 100, 99, 98,...or A, B, C?," Cowles Foundation Discussion Papers 1710, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1710
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    1. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    2. Alexis Direr, 2001. "Interdependent Preferences and Aggregate Saving," Annals of Economics and Statistics, GENES, issue 63-64, pages 297-308.
    3. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115(2), pages 338-363.
    4. Cole, Harold L. & Mailath, George J. & Postlewaite, Andrew, 1998. "Class systems and the enforcement of social norms," Journal of Public Economics, Elsevier, vol. 70(1), pages 5-35, October.
    5. Green, Jerry R & Stokey, Nancy L, 1983. "A Comparison of Tournaments and Contracts," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 349-364, June.
    6. Pollak, Robert A, 1976. "Interdependent Preferences," American Economic Review, American Economic Association, vol. 66(3), pages 309-320, June.
    7. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    8. Pradeep Dubey & John Geanakoplos, 2005. "Grading in Games of Status: Marking Exams and Setting Wages," Cowles Foundation Discussion Papers 1544, Cowles Foundation for Research in Economics, Yale University, revised Dec 2005.
    9. repec:adr:anecst:y:2001:i:63-64:p:15 is not listed on IDEAS
    10. Dominique Demougin & Claude Fluet & Carsten Helm, 2006. "Output and wages with inequality averse agents," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 39(2), pages 399-413, May.
    11. Corneo, Giacomo & Jeanne, Olivier, 1997. "On relative wealth effects and the optimality of growth," Economics Letters, Elsevier, vol. 54(1), pages 87-92, January.
    12. Dubey, Pradeep & Wu, Chien-wei, 2001. "Competitive prizes: when less scrutiny induces more effort," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 311-336, December.
    13. Ed Hopkins & Tatiana Kornienko, 2003. "Ratio Orderings and Comparative Statics," Edinburgh School of Economics Discussion Paper Series 91, Edinburgh School of Economics, University of Edinburgh.
    14. Englmaier, Florian & Wambach, Achim, 2010. "Optimal incentive contracts under inequity aversion," Games and Economic Behavior, Elsevier, vol. 69(2), pages 312-328, July.
    15. Frank, Robert H., 1993. "Choosing the Right Pond: Human Behavior and the Quest for Status," OUP Catalogue, Oxford University Press, number 9780195049459.
    16. Hideshi Itoh, 2004. "Moral Hazard and Other‐Regarding Preferences," The Japanese Economic Review, Japanese Economic Association, vol. 55(1), pages 18-45, March.
    17. Dubey, Pradeep & Haimanko, Ori, 2003. "Optimal scrutiny in multi-period promotion tournaments," Games and Economic Behavior, Elsevier, vol. 42(1), pages 1-24, January.
    18. Harold L. Cole & George J. Mailath & Andrew Postlewaite, 1995. "Incorporating concern for relative wealth into economic models," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 19(Sum), pages 12-21.
    19. Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-857, July.
    20. Cole, Harold L & Mailath, George J & Postlewaite, Andrew, 1992. "Social Norms, Savings Behavior, and Growth," Journal of Political Economy, University of Chicago Press, vol. 100(6), pages 1092-1125, December.
    21. Pradeep Dubey & John Geanakoplos, 2004. "Grading Exams: 100, 99, ..., 1 or A, B, C? Incentives in Games of Status," Cowles Foundation Discussion Papers 1467, Cowles Foundation for Research in Economics, Yale University.
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    More about this item

    Keywords

    Status; Grading; Incentives; Education; Exams;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • I20 - Health, Education, and Welfare - - Education - - - General
    • I30 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General

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