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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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  • Pivato, Marcus, 2011. "Voting rules as statistical estimators," MPRA Paper 30292, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:30292
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    Citations

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    Cited by:

    1. Ding, Huihui & Pivato, Marcus, 2021. "Deliberation and epistemic democracy," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 138-167.
    2. Malik Magdon-Ismail & Lirong Xia, 2018. "A Mathematical Model for Optimal Decisions in a Representative Democracy," Papers 1807.06157, arXiv.org.
    3. Marcus Pivato, 2016. "Asymptotic utilitarianism in scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 431-458, August.
    4. 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.
    5. Pivato, Marcus, 2015. "Condorcet meets Bentham," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 58-65.
    6. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    7. Marcus Pivato, 2016. "Statistical Utilitarianism," Studies in Political Economy, in: Maria Gallego & Norman Schofield (ed.), The Political Economy of Social Choices, pages 187-204, Springer.
    8. Irem Bozbay, 2015. "Truth-Tracking Judgment Aggregation Over Interconnected Issues," School of Economics Discussion Papers 0916, School of Economics, University of Surrey.
    9. Dietrich, Franz & Spiekermann, Kai, 2016. "Jury Theorems," MPRA Paper 72951, University Library of Munich, Germany.
    10. Irem Bozbay, 2019. "Truth-tracking judgment aggregation over interconnected issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 337-370, August.
    11. Nehring, Klaus & Pivato, Marcus, 2019. "Majority rule in the absence of a majority," Journal of Economic Theory, Elsevier, vol. 183(C), pages 213-257.
    12. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2015. "Distance rationalization of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 345-377, September.
    13. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    14. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    15. Andjiga, Nicolas G. & Mekuko, Aurelien Y. & Moyouwou, Issofa, 2014. "Metric rationalization of social welfare functions," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 14-23.
    16. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).
    17. Steve Alpern & Bo Chen, 2022. "Optimizing voting order on sequential juries: a median voter theorem and beyond," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(3), pages 527-565, April.

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    More about this item

    Keywords

    voting; maximum likelihood estimator; maximum a priori estimator; expected utility maximizer; statistics; epistemic democracy; Condorcet jury theorem; scoring rule;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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