IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Voting rules as statistical estimators

  • Marcus Pivato

    ()

We adopt an ‘epistemic’ interpretation of social decisions: there is an objectively correct choice, each voter receives a ‘noisy signal’ of the correct choice, and the social objective is to aggregate these signals to make the best possible guess about the correct choice. One epistemic method is to fix a probability model and compute the maximum likelihood estimator (MLE), maximum a posteriori (MAP) estimator or expected utility maximizer (EUM), given the data provided by the voters. We first show that an abstract voting rule can be interpreted as MLE or MAP if and only if it is a scoring rule. We then specialize to the case of distance-based voting rules, in particular, the use of the median rule in judgement aggregation. Finally, we show how several common ‘quasiutilitarian’ voting rules can be interpreted as EUM. Copyright Springer-Verlag 2013

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://hdl.handle.net/10.1007/s00355-011-0619-1
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 40 (2013)
Issue (Month): 2 (February)
Pages: 581-630

as
in new window

Handle: RePEc:spr:sochwe:v:40:y:2013:i:2:p:581-630
Contact details of provider: Web page: http://link.springer.de/link/service/journals/00355/index.htm

Order Information: Web: http://link.springer.de/orders.htm

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Pivato, Marcus, 2011. "Variable-population voting rules," MPRA Paper 31896, University Library of Munich, Germany.
  2. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, vol. 47(6), pages 1321-36, November.
  3. Michael Miller & Daniel Osherson, 2009. "Methods for distance-based judgment aggregation," Social Choice and Welfare, Springer, vol. 32(4), pages 575-601, May.
  4. Mongin, Philippe, 1998. "The paradox of the Bayesian experts and state-dependent utility theory," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 331-361, April.
  5. Itzhak Gilboa & Dov Samet & David Schmeidler, 2001. "Utilitarian Aggregation of Beliefs and Tastes," Game Theory and Information 0105001, EconWPA.
  6. Michel Balinski & Rida Laraki, 2011. "Majority Judgment: Measuring, Ranking, and Electing," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015137, June.
  7. Stephen Gordon & Michel Truchon, 2008. "Social choice, optimal inference and figure skating," Social Choice and Welfare, Springer, vol. 30(2), pages 265-284, February.
  8. Ruth Ben-Yashar & Jacob Paroush, 2001. "Optimal decision rules for fixed-size committees in polychotomous choice situations," Social Choice and Welfare, Springer, vol. 18(4), pages 737-746.
  9. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
  10. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
  11. Michel Truchon & Stephen Gordon, 2006. "Statistical Comparison of Aggregation Rules for Votes," Cahiers de recherche 0625, CIRPEE.
  12. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
  13. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
  14. Chambers, Christopher & Takashi Hayashi, 2003. "Preference Aggregation under Uncertainty: Savage vs. Pareto," Working Papers 1184, California Institute of Technology, Division of the Humanities and Social Sciences.
  15. Hartmann, Stephan & Pigozzi, Gabriella & Sprenger, Jan, 2010. "Reliable Methods of Judgement Aggregation," Economics Papers from University Paris Dauphine 123456789/6413, Paris Dauphine University.
  16. MONGIN, Philippe, 1993. "Consistent Bayesian Aggregation," CORE Discussion Papers 1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Michel Truchon, 2006. "Borda and the Maximum Likelihood Approach to Vote Aggregation," Cahiers de recherche 0623, CIRPEE.
  18. Drissi, Mohamed & Truchon, Michel, 2002. "Maximum Likelihood Approach to Vote Aggregation with Variable Probabilities," Cahiers de recherche 0211, Université Laval - Département d'économique.
  19. Franz Dietrich, 2006. "General Representation of Epistemically Optimal Procedures," Social Choice and Welfare, Springer, vol. 26(2), pages 263-283, April.
  20. Serguei Kaniovski, 2010. "Aggregation of correlated votes and Condorcet’s Jury Theorem," Theory and Decision, Springer, vol. 69(3), pages 453-468, September.
  21. Patrick Hummel, 2010. "Jury theorems with multiple alternatives," Social Choice and Welfare, Springer, vol. 34(1), pages 65-103, January.
  22. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
  23. Michael Fligner & Joseph Verducci, 1990. "Posterior probabilities for a consensus ordering," Psychometrika, Springer, vol. 55(1), pages 53-63, March.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:40:y:2013:i:2:p:581-630. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn)

or (Christopher F Baum)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.