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Voting rules as statistical estimators

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  • Pivato, Marcus

Abstract

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 estimator (MAP) 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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 30292.

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Date of creation: 13 Apr 2011
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Handle: RePEc:pra:mprapa:30292

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Keywords: voting; maximum likelihood estimator; maximum a priori estimator; expected utility maximizer; statistics; epistemic democracy; Condorcet jury theorem; scoring rule;

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References

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  1. Truchon, Michel, 2008. "Borda and the maximum likelihood approach to vote aggregation," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 96-102, January.
  2. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
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  19. Drissi, Mohamed & Truchon, Michel, 2002. "Maximum Likelihood Approach to Vote Aggregation with Variable Probabilities," Cahiers de recherche 0211, Université Laval - Département d'économique.
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Cited by:
  1. Pivato, Marcus, 2011. "Variable-population voting rules," MPRA Paper 31896, University Library of Munich, Germany.
  2. Pivato, Marcus, 2013. "Statistical utilitarianism," MPRA Paper 49561, University Library of Munich, Germany.
  3. Dietrich, Franz, 2011. "Scoring rules for judgment aggregation," MPRA Paper 35657, University Library of Munich, Germany.

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