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Voting rules as statistical estimators

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  • Marcus Pivato

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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 (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

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:40:y:2013:i:2:p:581-630
    DOI: 10.1007/s00355-011-0619-1
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. Pivato, Marcus, 2015. "Condorcet meets Bentham," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 58-65.
    3. 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.
    4. 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.
    5. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    6. repec:eee:mateco:v:72:y:2017:i:c:p:51-69 is not listed on IDEAS
    7. 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.
    8. Pivato, Marcus, 2013. "Statistical utilitarianism," MPRA Paper 49561, University Library of Munich, Germany.
    9. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    10. 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.
    11. Dietrich, Franz & Spiekermann, Kai, 2016. "Jury Theorems," MPRA Paper 72951, University Library of Munich, Germany.

    More about this item

    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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