IDEAS home Printed from https://ideas.repec.org/p/mal/wpaper/2009-2.html
   My bibliography  Save this paper

Picking the Winners

Author

Listed:
  • Pablo Amorós

    (Department of Economic Theory, Universidad de Málaga)

Abstract

We analyze the problem of choosing the w contestants who will win a competition within a group of n>w competitors when all jurors commonly observe who are the w best contestants but may be biased. We study conditions on the configuration of the jury so that it is possible to induce the jurors to always choose the best contestants, whoever they are. If the equilibrium concept used by the jurors is dominant strategies, the necessary and sufficient conditions incorporate very strong informational requirements on the mechanism designer. If we relax the equilibrium concept to Nash or subgame perfect equilibria the necessary and sufficient conditions are less demanding. Moreover, these conditions are also necessary for any other equilibrium concept. Finally, we study one specific application: we propose a simple and natural mechanism for the case where each juror is biased in favor of one and only one (different) contestant.

Suggested Citation

  • Pablo Amorós, 2009. "Picking the Winners," Working Papers 2009-2, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    • Handle: RePEc:mal:wpaper:2009-2
    as

    Download full text from publisher

    File URL: https://theeconomics.uma.es/malagawpseries/Papers/METCwp2009-2.pdf
    File Function: First version, 2009
    Download Restriction: no
    File URL: https://theeconomics.uma.es/malagawpseries/Papers/METCwp2009-6.pdf
    File Function: Revised version, 2010
    Download Restriction: no
    ---><---

    Other versions of this item:

    • Pablo Amorós, 2010. "Picking the Winners," Working Papers 2010-06, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.

    References listed on IDEAS

    as
    1. Martinelli, Cesar, 2002. "Convergence Results for Unanimous Voting," Journal of Economic Theory, Elsevier, vol. 105(2), pages 278-297, August.
    2. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    3. Kaminski, Marek M., 2006. "Parametric rationing methods," Games and Economic Behavior, Elsevier, vol. 54(1), pages 115-133, January.
    4. Austen-Smith, David & Banks, Jeffrey S., 1996. "Information Aggregation, Rationality, and the Condorcet Jury Theorem," American Political Science Review, Cambridge University Press, vol. 90(1), pages 34-45, March.
    5. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    6. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    7. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    8. Saijo, Tatsuyoshi, 1988. "Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation," Econometrica, Econometric Society, vol. 56(3), pages 693-700, May.
    9. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, vol. 65(5), pages 1029-1058, September.
    10. Duggan, John & Martinelli, Cesar, 2001. "A Bayesian Model of Voting in Juries," Games and Economic Behavior, Elsevier, vol. 37(2), pages 259-294, November.
    11. Amoros, Pablo & Corchon, Luis C. & Moreno, Bernardo, 2002. "The Scholarship Assignment Problem," Games and Economic Behavior, Elsevier, vol. 38(1), pages 1-18, January.
    12. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 757-775.
    13. Feddersen, Timothy J & Pesendorfer, Wolfgang, 1996. "The Swing Voter's Curse," American Economic Review, American Economic Association, vol. 86(3), pages 408-424, June.
    14. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    15. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    16. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Hendrickx, R.L.P., 2005. "Balanced Contributions for Multi-Issue Allocation Situations," Discussion Paper 2005-93, Tilburg University, Center for Economic Research.
    17. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    18. Wolinsky, Asher, 2002. "Eliciting information from multiple experts," Games and Economic Behavior, Elsevier, vol. 41(1), pages 141-160, October.
    19. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    20. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    21. Gerardi, Dino & McLean, Richard & Postlewaite, Andrew, 2009. "Aggregation of expert opinions," Games and Economic Behavior, Elsevier, vol. 65(2), pages 339-371, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Amorós, Pablo, 2023. "Evaluation and strategic manipulation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    2. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    3. Amorós, Pablo, 2009. "Eliciting socially optimal rankings from unfair jurors," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1211-1226, May.
    4. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    5. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    6. Corchón, Luis C., 2008. "The theory of implementation : what did we learn?," UC3M Working papers. Economics we081207, Universidad Carlos III de Madrid. Departamento de Economía.
    7. Xiong, Siyang, 2021. "Designing referenda: An economist's pessimistic perspective," Journal of Economic Theory, Elsevier, vol. 191(C).
    8. Pablo Amorós & Ricardo Martínez & Bernardo Moreno & M. Puy, 2012. "Deciding whether a law is constitutional, interpretable, or unconstitutional," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 1-14, March.
    9. Paolo Balduzzi & Clara Graziano & Annalisa Luporini, 2014. "Voting in small committees," Journal of Economics, Springer, vol. 111(1), pages 69-95, February.
    10. Michele Lombardi & Naoki Yoshihara, 2013. "A full characterization of nash implementation with strategy space reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 131-151, September.
    11. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
    12. Saran, Rene & Tumennasan, Norovsambuu, 2013. "Whose opinion counts? Implementation by sortition," Games and Economic Behavior, Elsevier, vol. 78(C), pages 72-84.
    13. Hao Li & Sherwin Rosen & Wing Suen, 2001. "Conflicts and Common Interests in Committees," American Economic Review, American Economic Association, vol. 91(5), pages 1478-1497, December.
    14. Sinan Ertemel & Rajnish Kumar, 2018. "Proportional rules for state contingent claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 229-246, March.
    15. Rene Saran & Norovsambuu Tumennasan, 2011. "Whose Opinion Counts? Political Processes and the Implementation Problem," Economics Working Papers 2011-06, Department of Economics and Business Economics, Aarhus University.
    16. Gerling, Kerstin & Gruner, Hans Peter & Kiel, Alexandra & Schulte, Elisabeth, 2005. "Information acquisition and decision making in committees: A survey," European Journal of Political Economy, Elsevier, vol. 21(3), pages 563-597, September.
    17. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    18. Amorós, Pablo, 2016. "Subgame perfect implementation of the deserving winner of a competition with natural mechanisms," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 44-57.
    19. Yamato, Takehiko, 1999. "Nash implementation and double implementation: equivalence theorems1," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 215-238, March.
    20. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.

    More about this item

    Keywords

    Mechanism design; Social choice;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mal:wpaper:2009-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ascension Andina (email available below). General contact details of provider: https://edirc.repec.org/data/dtmales.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.