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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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    File URL: http://cowles.econ.yale.edu/P/cd/d17a/d1710.pdf
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    Bibliographic Info

    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1710.

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    Length: 37 pages
    Date of creation: Jun 2009
    Date of revision:
    Publication status: Published in Games and Economic Behavior (2010), 69(1): 72-94
    Handle: RePEc:cwl:cwldpp:1710

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    Keywords: Status; Grading; Incentives; Education; Exams;

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    1. Dominique Demougin & Claude Fluet & Carsten Helm, 2004. "Output and Wages with Inequality Averse Agents," CIRANO Working Papers 2004s-47, CIRANO.
    2. Hideshi Itoh, 2004. "Moral Hazard and Other-Regarding Preferences," The Japanese Economic Review, Japanese Economic Association, vol. 55(1), pages 18-45.
    3. 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 349-64, June.
    4. Pollak, Robert A, 1976. "Interdependent Preferences," American Economic Review, American Economic Association, vol. 66(3), pages 309-20, June.
    5. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    6. Harold L. Cole & George J. Mailath & Andrew Postlewaite, 1995. "Incorporating concern for relative wealth into economic models," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Sum, pages 12-21.
    7. Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-57, July.
    8. Englmaier, Florian & Wambach, Achim, 2010. "Optimal incentive contracts under inequity aversion," Games and Economic Behavior, Elsevier, vol. 69(2), pages 312-328, July.
    9. 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.
    10. 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.
    11. Harold L. Cole & George J. Mailath & Andrew Postlewaite, . ""Class Systems and the Enforcement of Social Norms''," CARESS Working Papres 96-04, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    12. 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.
    13. Alexis DIRER, 2001. "Interdependent Preferences and Aggregate Saving," Annales d'Economie et de Statistique, ENSAE, issue 63-64, pages 297-308.
    14. Ed Hopkins & Tatiana Kornienko, 2004. "Ratio Orderings and Comparative Statics," ESE Discussion Papers 91, Edinburgh School of Economics, University of Edinburgh.
    15. Corneo, Giacomo & Jeanne, Olivier, 1997. "On relative wealth effects and the optimality of growth," Economics Letters, Elsevier, vol. 54(1), pages 87-92, January.
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