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On the informational efficiency of simple scoring rules

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  • Goertz, Johanna M.M.
  • Maniquet, François

Abstract

We study information aggregation in large elections. With two candidates, efficient information aggregation is possible (e.g., Feddersen and Pesendorfer [5], [6] and [7]). We show that this result does not extend to elections with more than two candidates. We study a class of simple scoring rules in voting games with Poisson population uncertainty and three candidates. No simple scoring rule aggregates information efficiently, even if preferences are dichotomous and a Condorcet winner always exists. We introduce a weaker criterion of informational efficiency that requires a voting rule to have at least one efficient equilibrium. Only approval voting satisfies this criterion.

Suggested Citation

  • Goertz, Johanna M.M. & Maniquet, François, 2011. "On the informational efficiency of simple scoring rules," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1464-1480, July.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1464-1480
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    References listed on IDEAS

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    1. repec:cup:apsrev:v:93:y:1999:i:02:p:381-398_21 is not listed on IDEAS
    2. Goertz, Johanna M.M. & Maniquet, François, 2011. "On the informational efficiency of simple scoring rules," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1464-1480, July.
    3. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    4. 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.
    5. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    6. Feddersen, Timothy J & Pesendorfer, Wolfgang, 1996. "The Swing Voter's Curse," American Economic Review, American Economic Association, vol. 86(3), pages 408-424, June.
    7. Jean-François Laslier, 2009. "The Leader rule: a model of strategic approval voting in a large electorate," Post-Print hal-00363218, HAL.
    8. repec:cup:apsrev:v:92:y:1998:i:01:p:23-35_20 is not listed on IDEAS
    9. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    10. repec:cup:apsrev:v:87:y:1993:i:01:p:102-114_09 is not listed on IDEAS
    11. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    12. repec:cup:apsrev:v:72:y:1978:i:03:p:831-847_15 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Sébastien Courtin & Matias Nunez, 2013. "A Map of Approval Voting Equilibria Outcomes," THEMA Working Papers 2013-31, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2016. "Divided majority and information aggregation: Theory and experiment," Journal of Public Economics, Elsevier, vol. 134(C), pages 114-128.
    3. Ahn, David S. & Oliveros, Santiago, 2016. "Approval voting and scoring rules with common values," Journal of Economic Theory, Elsevier, vol. 166(C), pages 304-310.
    4. Goertz, Johanna M.M. & Maniquet, François, 2011. "On the informational efficiency of simple scoring rules," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1464-1480, July.
    5. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    6. Bozbay, İrem & Dietrich, Franz & Peters, Hans, 2014. "Judgment aggregation in search for the truth," Games and Economic Behavior, Elsevier, vol. 87(C), pages 571-590.
    7. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 157-189, May.
    8. Arnaud Dellis & Mandar Oak, 2016. "Multiple votes, multiple candidacies and polarization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 1-38, January.
    9. François Maniquet & Massimo Morelli, 2015. "Approval quorums dominate participation quorums," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 1-27, June.
    10. Matías Núñez & Jean Laslier, 2014. "Preference intensity representation: strategic overstating in large elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 313-340, February.
    11. Ferrari, Luca, 2016. "How partisan voters fuel the influence of public information," Economics Letters, Elsevier, vol. 149(C), pages 157-160.
    12. Sébastien Courtin & Matías Núñez, 2017. "Dominance solvable approval voting games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(6), pages 1047-1068, December.
    13. repec:esx:essedp:732 is not listed on IDEAS
    14. Matias Nunez & Laslier Jean François Author-Workplace-Name : Ecole Polytechnique, 2010. "Overstating: A tale of two cities," THEMA Working Papers 2010-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    15. Herman Demeze & Issofa Moyouwou & Roland Pongou, 2016. "The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis," Working Papers 1611e, University of Ottawa, Department of Economics.
    16. Ginzburg, Boris, 2017. "Sincere voting in an electorate with heterogeneous preferences," Economics Letters, Elsevier, vol. 154(C), pages 120-123.
    17. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, January.
    18. GOERTZ, Johanna & MANIQUET, François, 2013. "Large elections with multiple alternatives: a Condorcet Jury Theorem and inefficient equilibria," CORE Discussion Papers 2013023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. J. Goertz, 2014. "Inefficient committees: small elections with three alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 357-375, August.
    20. Johanna Goertz & Francois Maniquet, 2011. "On a Three-Alternative Condorcet Jury Theorem," CESifo Working Paper Series 3457, CESifo Group Munich.
    21. Demeze, Herman & Moyouwou, Issofa & Pongou, Roland, 2016. "The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis," MPRA Paper 70607, University Library of Munich, Germany.
    22. Boris Ginzburg & José-Alberto Guerra, 2017. "When Ignorance is Bliss: Theory and Experiment on Collective Learning," DOCUMENTOS CEDE 015377, UNIVERSIDAD DE LOS ANDES-CEDE.
    23. Goertz, Johanna M.M. & Maniquet, François, 2014. "Condorcet Jury Theorem: An example in which informative voting is rational but leads to inefficient information aggregation," Economics Letters, Elsevier, vol. 125(1), pages 25-28.

    More about this item

    Keywords

    Efficient information aggregation Scoring rules Poisson games Approval voting;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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