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One person, one weight: when is weighted voting democratic?

Author

Listed:
  • Roy Baharad

    (The Hebrew University of Jerusalem)

  • Shmuel Nitzan

    (Bar-Ilan University)

  • Erel Segal-Halevi

    (Ariel University)

Abstract

In a classical “jury theorem” setting, the collective performance of a group of independent decision-makers is maximized by a voting rule that assigns weight to individuals compatibly with skills. The primary concern is that such weighted voting interferes with majoritarianism, since excessive power may be granted to a competent minority. In this paper, we address a surprisingly undertheorized issue of much significance to collective decision-making: the overlap of optimal weighted voting and the democratic, ubiquitous simple majority rule which is typically adopted in public decision-making. Running Monte Carlo simulations on the distribution of skills in large groups, our main findings are rather counterintuitive. In terms of procedure, the optimal allocation of weights is almost always democratic or “semi-democratic”, in that it satisfies or draws close to “one person, one weight”. In terms of outcome, the chosen alternative under optimal weighted voting is almost always the one that would have been selected by the simple majority rule, which satisfies “one person, one vote”. We thereby submit that the decision rules supported by the proceduralist and epistemic approaches to collective decision-making, effectively coincide more often than one would expect.

Suggested Citation

  • Roy Baharad & Shmuel Nitzan & Erel Segal-Halevi, 2022. "One person, one weight: when is weighted voting democratic?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 467-493, August.
  • Handle: RePEc:spr:sochwe:v:59:y:2022:i:2:d:10.1007_s00355-022-01393-8
    DOI: 10.1007/s00355-022-01393-8
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    References listed on IDEAS

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    1. Lloyd Shapley & Bernard Grofman, 1984. "Optimizing group judgmental accuracy in the presence of interdependencies," Public Choice, Springer, vol. 43(3), pages 329-343, January.
    2. Dietrich, F.K. & Spiekermann, K., 2010. "Epistemic democracy with defensible premises," Research Memorandum 066, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Nitzan, Shmuel & Paroush, Jacob, 1982. "Optimal Decision Rules in Uncertain Dichotomous Choice Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 289-297, June.
    4. Franz Dietrich, 2006. "General Representation of Epistemically Optimal Procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 263-283, April.
    5. Ben-Yashar, Ruth C & Nitzan, Shmuel I, 1997. "The Optimal Decision Rule for Fixed-Size Committees in Dichotomous Choice Situations: The General Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 175-186, February.
    6. Rae, Douglas W., 1969. "Decision-Rules and Individual Values in Constitutional Choice," American Political Science Review, Cambridge University Press, vol. 63(1), pages 40-56, March.
    7. Dietrich, Franz & Spiekermann, Kai, 2013. "Epistemic Democracy With Defensible Premises1," Economics and Philosophy, Cambridge University Press, vol. 29(1), pages 87-120, March.
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    Cited by:

    1. Ben Abramowitz & Omer Lev & Nicholas Mattei, 2022. "Who Reviews The Reviewers? A Multi-Level Jury Problem," Papers 2211.08494, arXiv.org, revised Dec 2023.

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