IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v23y2004i2p161-185.html
   My bibliography  Save this article

Maximum likelihood approach to vote aggregation with variable probabilities

Author

Listed:
  • Mohamed Drissi-Bakhkhat
  • Michel Truchon

Abstract

The Condorcet-Kemeny-Young statistical approach to vote aggregation is based on the assumption that voters have the same probability of comparing correctly two alternatives and that this probability is the same for any pair of alternatives. We relax the second part of this assumption by letting the probability of comparing correctly two alternatives be increasing with the distance between two alternatives in the allegedly true ranking. This leads to a rule in which the majority in favor of one alternative against another one is given a larger weight the larger the distance between the two alternatives in the true ranking, i.e., the larger the probability that the voters compare them correctly. This rule is not Condorcet consistent and does not satisfy local independence of irrelevant alternatives. Yet, it is anonymous, neutral, and paretian. It also appears that its performance in selecting the alternative most likely to be the best improves with the rate at which the probability increases. Copyright Springer-Verlag 2004

Suggested Citation

  • Mohamed Drissi-Bakhkhat & Michel Truchon, 2004. "Maximum likelihood approach to vote aggregation with variable probabilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 161-185, October.
    • Handle: RePEc:spr:sochwe:v:23:y:2004:i:2:p:161-185
    DOI: 10.1007/s00355-003-0242-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00355-003-0242-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00355-003-0242-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Berg, Sven, 1994. "Evaluation of some weighted majority decision rules under dependent voting," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 71-83, October.
    2. Nitzan, Shmuel & Paroush, Jacob, 1982. "Optimal Decision Rules in Uncertain Dichotomous Choice Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 289-297, June.
    3. Ladha, Krishna K., 1995. "Information pooling through majority-rule voting: Condorcet's jury theorem with correlated votes," Journal of Economic Behavior & Organization, Elsevier, vol. 26(3), pages 353-372, May.
    4. Truchon, M., 1998. "Figure Skating and the Theory of Social Choice," Papers 9814, Laval - Recherche en Politique Economique.
    5. Truchon, Michel, 1998. "An Extension of the Concordet Criterion and Kemeny Orders," Cahiers de recherche 9813, Université Laval - Département d'économique.
    6. Donald G. Saari & Vincent R. Merlin, 2000. "A geometric examination of Kemeny's rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 403-438.
    7. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
    8. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    2. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    3. Marcus Hagedorn & Tzuo Hann Law & Iourii Manovskii, 2017. "Identifying Equilibrium Models of Labor Market Sorting," Econometrica, Econometric Society, vol. 85, pages 29-65, January.
    4. Jean-François Laslier, 2010. "In Silico Voting Experiments," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 311-335, Springer.
    5. Truchon, Michel, 2008. "Borda and the maximum likelihood approach to vote aggregation," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 96-102, January.
    6. Truchon, Michel, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0402, Université Laval - Département d'économique.
    7. Conitzer, Vincent, 2012. "Should social network structure be taken into account in elections?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 100-102.
    8. T. Tideman & Florenz Plassmann, 2014. "Which voting rule is most likely to choose the “best” candidate?," Public Choice, Springer, vol. 158(3), pages 331-357, March.
    9. Yuta Nakamura, 2015. "Maximum Likelihood Social Choice Rule," The Japanese Economic Review, Japanese Economic Association, vol. 66(2), pages 271-284, June.

    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. Ruth Ben-Yashar, 2006. "Information is important to Condorcet jurors," Public Choice, Springer, vol. 127(3), pages 305-319, June.
    2. Bezalel Peleg & Shmuel Zamir, 2012. "Extending the Condorcet Jury Theorem to a general dependent jury," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 91-125, June.
    3. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    4. Giuseppe Munda, 2012. "Choosing Aggregation Rules for Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 109(3), pages 337-354, December.
    5. Ruth Ben-Yashar & Leif Danziger, 2015. "When is voting optimal?," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 341-356, October.
    6. Ben-Yashar, Ruth & Khuller, Samir & Kraus, Sarit, 2001. "Optimal collective dichotomous choice under partial order constraints," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 349-364, May.
    7. Alexander Lundberg, 2020. "The importance of expertise in group decisions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 495-521, October.
    8. Hummel, Patrick, 2011. "Information aggregation in multicandidate elections under plurality rule and runoff voting," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 1-6, July.
    9. Bezalel Peleg & Shmuel Zamir, 2009. "On Bayesian-Nash Equilibria Satisfying the Condorcet Jury Theorem: The Dependent Case," Discussion Paper Series dp527, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    10. Truchon, Michel, 1998. "Figure Skating and the Theory of Social Choice," Cahiers de recherche 9814, Université Laval - Département d'économique.
    11. Eyal Baharad & Jacob Goldberger & Moshe Koppel & Shmuel Nitzan, 2012. "Beyond Condorcet: optimal aggregation rules using voting records," Theory and Decision, Springer, vol. 72(1), pages 113-130, January.
    12. Patrick Hummel, 2012. "Deliberation in large juries with diverse preferences," Public Choice, Springer, vol. 150(3), pages 595-608, March.
    13. Conitzer, Vincent, 2012. "Should social network structure be taken into account in elections?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 100-102.
    14. Baharad, Eyal & Ben-Yashar, Ruth & Patal, Tal, 2020. "On the merit of non-specialization in the context of majority voting," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 128-133.
    15. Bezalel Peleg & Shmuel Zamir, 2008. "Condorcet Jury Theorem: The Dependent Case," Levine's Working Paper Archive 122247000000002422, David K. Levine.
    16. Ruth Ben-Yashar & Igal Milchtaich, 2007. "First and second best voting rules in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 453-486, October.
    17. Ruth Ben‐Yashar & Miriam Krausz & Shmuel Nitzan, 2018. "Government loan guarantees and the credit decision‐making structure," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(2), pages 607-625, May.
    18. Azzini, Ivano & Munda, Giuseppe, 2020. "A new approach for identifying the Kemeny median ranking," European Journal of Operational Research, Elsevier, vol. 281(2), pages 388-401.
    19. BAHARAD, Eyal & BEN-YASHAR, Ruth & NITZAN, Shmuel, 2018. "Variable Competence and Collective Performance: Unanimity vs. Simple Majority Rule," Discussion paper series HIAS-E-80, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    20. Truchon, Michel, 1999. "La démocratie : oui, mais laquelle?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 75(1), pages 189-214, mars-juin.

    More about this item

    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:spr:sochwe:v:23:y:2004:i:2:p:161-185. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.