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Beyond Condorcet: optimal aggregation rules using voting records

  • Eyal Baharad

    ()

  • Jacob Goldberger

    ()

  • Moshe Koppel

    ()

  • Shmuel Nitzan

    ()

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-maker's capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This paper presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters' past decisions is available, but the correct decisions are not known. We observe that any arbitrary evaluation of the decision-maker's capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers.

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File URL: http://hdl.handle.net/10.1007/s11238-010-9240-5
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Article provided by Springer in its journal Theory and Decision.

Volume (Year): 72 (2012)
Issue (Month): 1 (January)
Pages: 113-130

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Handle: RePEc:kap:theord:v:72:y:2012:i:1:p:113-130
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  1. Ruth Ben-Yashar & Igal Milchtaich, 2007. "First and second best voting rules in committees," Social Choice and Welfare, Springer, vol. 29(3), pages 453-486, October.
  2. Owen, Guillermo & Grofman, Bernard & Feld, Scott L., 1989. "Proving a distribution-free generalization of the Condorcet Jury Theorem," Mathematical Social Sciences, Elsevier, vol. 17(1), pages 1-16, February.
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  6. Ronen Bar-El & Teresa García-Muñoz & Shoshana Neuman & Yossef Tobol, 2010. "The Evolution of Secularization: Cultural Transmission, Religion and Fertility. Theory, Simulations and Evidence," Papers on Economics of Religion 10/03, Department of Economic Theory and Economic History of the University of Granada..
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  10. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  11. Leonid V. Azarnert, 2008. "Involuntary Integration in Public Education, Fertility and Human Capital," Working Papers 2008-07, Bar-Ilan University, Department of Economics.
  12. Lloyd Shapley & Bernard Grofman, 1984. "Optimizing group judgmental accuracy in the presence of interdependencies," Public Choice, Springer, vol. 43(3), pages 329-343, January.
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