Voting rules as statistical estimators
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
Volume (Year): 40 (2013)
Issue (Month): 2 (February)
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- Pivato, Marcus, 2011.
"Variable-population voting rules,"
31896, University Library of Munich, Germany.
- 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.
- Michael Miller & Daniel Osherson, 2009. "Methods for distance-based judgment aggregation," Social Choice and Welfare, Springer, vol. 32(4), pages 575-601, May.
- 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.
- MONGIN, Philippe, 1996. "The Paradox of the Bayesian Experts and State-Dependent Utility Theory," CORE Discussion Papers 1996026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- P. Mongin., 1997. "The paradox of the Bayesian experts and state-dependent utility theory," THEMA Working Papers 97-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- MONGIN, Philippe, . "The paradox of the Bayesian experts and state-dependent utility theory," CORE Discussion Papers RP -1312, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Itzhak Gilboa & Dov Samet & David Schmeidler, 2001.
"Utilitarian Aggregation of Beliefs and Tastes,"
Game Theory and Information
- Michel Balinski & Rida Laraki, 2011. "Majority Judgment: Measuring, Ranking, and Electing," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015137, June.
- Stephen Gordon & Michel Truchon, 2008.
"Social choice, optimal inference and figure skating,"
Social Choice and Welfare,
Springer, vol. 30(2), pages 265-284, February.
- Stephen Gordon & Michel Truchon, 2006. "Social Choice, Optimal Inference and Figure Skating," Cahiers de recherche 0624, CIRPEE.
- 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.
- 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.
- 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.
- Michel Truchon & Stephen Gordon, 2006.
"Statistical Comparison of Aggregation Rules for Votes,"
Cahiers de recherche
- Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
- Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
- 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.
- Chambers, Christopher & Takashi Hayashi, 2003.
"Preference Aggregation under Uncertainty: Savage vs. Pareto,"
1184, California Institute of Technology, Division of the Humanities and Social Sciences.
- Chambers, Christopher P. & Hayashi, Takashi, 2006. "Preference aggregation under uncertainty: Savage vs. Pareto," Games and Economic Behavior, Elsevier, vol. 54(2), pages 430-440, February.
- Hartmann, Stephan & Pigozzi, Gabriella & Sprenger, Jan, 2010. "Reliable Methods of Judgement Aggregation," Economics Papers from University Paris Dauphine 123456789/6413, Paris Dauphine University.
- MONGIN, Philippe, 1993.
"Consistent Bayesian Aggregation,"
CORE Discussion Papers
1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Michel Truchon, 2006.
"Borda and the Maximum Likelihood Approach to Vote Aggregation,"
Cahiers de recherche
- Truchon, Michel, 2008. "Borda and the maximum likelihood approach to vote aggregation," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 96-102, January.
- Drissi, Mohamed & Truchon, Michel, 2002.
"Maximum Likelihood Approach to Vote Aggregation with Variable Probabilities,"
Cahiers de recherche
0211, Université Laval - Département d'économique.
- Mohamed Drissi-Bakhkhat & Michel Truchon, 2004. "Maximum likelihood approach to vote aggregation with variable probabilities," Social Choice and Welfare, Springer, vol. 23(2), pages 161-185, October.
- Franz Dietrich, 2006. "General Representation of Epistemically Optimal Procedures," Social Choice and Welfare, Springer, vol. 26(2), pages 263-283, April.
- Serguei Kaniovski, 2010. "Aggregation of correlated votes and Condorcet’s Jury Theorem," Theory and Decision, Springer, vol. 69(3), pages 453-468, September.
- Patrick Hummel, 2010. "Jury theorems with multiple alternatives," Social Choice and Welfare, Springer, vol. 34(1), pages 65-103, January.
- Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
- Michael Fligner & Joseph Verducci, 1990. "Posterior probabilities for a consensus ordering," Psychometrika, Springer, vol. 55(1), pages 53-63, March.
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