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On the Justice of Decision Rules

Author

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  • Jose Apesteguia
  • Miguel A. Ballester
  • Rosa Ferrer

Abstract

Which decision rules are the most efficient? Which are the best in terms of maximin or maximax? We study these questions for the case of a group of individuals faced with a collective choice from a set of alternatives. A key message from our results is that the set of optimal decision rules is well defined, particularly simple, and well known: the class of scoring rules. We provide the optimal scoring rules for the three different ideals of justice under consideration: utilitarianism (efficiency), maximin, and maximax. The optimal utilitarian scoring rule depends crucially on the probability distribution of the utilities. The optimal maximin (respectively maximax) scoring rule takes the optimal utilitarian scoring rule and applies a factor that shifts it towards negative voting (respectively plurality voting). Copyright 2011, Oxford University Press.

Suggested Citation

  • Jose Apesteguia & Miguel A. Ballester & Rosa Ferrer, 2011. "On the Justice of Decision Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 1-16.
    • Handle: RePEc:oup:restud:v:78:y:2011:i:1:p:1-16
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    File URL: http://hdl.handle.net/10.1093/restud/rdq023
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    Citations

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    Cited by:

    1. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 688-717.
    2. Kwiek, Maksymilian, 2014. "Efficient voting with penalties," Discussion Paper Series In Economics And Econometrics 1419, Economics Division, School of Social Sciences, University of Southampton.
    3. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    4. Apesteguia, Jose & Ballester, Miguel A. & Masatlioglu, Yusufcan, 2014. "A foundation for strategic agenda voting," Games and Economic Behavior, Elsevier, vol. 87(C), pages 91-99.
    5. 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.
    6. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    7. Miguel Ballester & Pedro Rey-Biel, 2009. "Does uncertainty lead to sincerity? Simple and complex voting mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 477-494, September.
    8. Tobias Rachidi, 2020. "Optimal Voting Mechanisms on Generalized Single-Peaked Domains," CRC TR 224 Discussion Paper Series crctr224_2020_214, University of Bonn and University of Mannheim, Germany.
    9. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1067-1088, November.
    10. Sandro Ambuehl & B. Douglas Bernheim, 2021. "Interpreting the will of the people: social preferences over ordinal outcomes," ECON - Working Papers 395, Department of Economics - University of Zurich, revised Jan 2024.
    11. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
    12. Nuñez, M. & Valletta, G., 2012. "The information simplicity of scoring rules," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. 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.
    14. Kwiek, Maksymilian, 2017. "Efficient voting with penalties," Games and Economic Behavior, Elsevier, vol. 104(C), pages 468-485.
    15. Kwiek, Maksymilian, 2014. "Conclave," European Economic Review, Elsevier, vol. 70(C), pages 258-275.
    16. Apesteguia, Jose & Ballester, Miguel A., 2012. "Welfare of naive and sophisticated players in school choice," Economics Letters, Elsevier, vol. 115(2), pages 172-174.
    17. Semin Kim, 2016. "Ordinal Versus Cardinal Voting Rules: A Mechanism Design Approach," Working papers 2016rwp-94, Yonsei University, Yonsei Economics Research Institute.
    18. Grofman, Bernard & Feld, Scott L. & Fraenkel, Jon, 2017. "Finding the Threshold of Exclusion for all single seat and multi-seat scoring rules: Illustrated by results for the Borda and Dowdall rules," Mathematical Social Sciences, Elsevier, vol. 85(C), pages 52-56.
    19. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(4), pages 1067-1088, November.
    20. Giles, Adam & Postl, Peter, 2014. "Equilibrium and effectiveness of two-parameter scoring rules," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 31-52.
    21. Sandro Ambuehl & B. Douglas Bernheim, 2021. "Interpreting the Will of the People - A Positive Analysis of Ordinal Preference Aggregation," CESifo Working Paper Series 9317, CESifo.

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