Beyond Condorcet: optimal aggregation rules using voting records
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.
(This abstract was borrowed from another version of this item.)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
- Daniel Berend & Jacob Paroush, 1998. "When is Condorcet's Jury Theorem valid?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 481-488.
- Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
- 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 289-97, June.
- Steven Brams & Peter Fishburn, 2005.
"Going from theory to practice: the mixed success of approval voting,"
Social Choice and Welfare,
Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 457-474, December.
- Brams, S.J. & Fishburn, P.C., 2003. "Going from Theory to Practice: The Mixed Success of Approval Voting," Working Papers 03-06, C.V. Starr Center for Applied Economics, New York University.
- Bar-El, Ronen & García-Muñoz, Teresa & Neuman, Shoshana & Tobol, Yossi, 2010.
"The Evolution of Secularization: Cultural Transmission, Religion and Fertility Theory, Simulations and Evidence,"
IZA Discussion Papers
4980, Institute for the Study of Labor (IZA).
- Ronen Bar-El & Teresa García-Muñoz & Shoshana Neuman & Yossef Tobol, 2013. "The evolution of secularization: cultural transmission, religion and fertility—theory, simulations and evidence," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(3), pages 1129-1174, July.
- Ronen Bar-El & Teresa García-Muñoz & Shoshana Neuman & Yossef Tobol, 2010. "The Evolution of Secularization: Cultural Transmission, Religion and Fertility Theory, Simulations and Evidence," Working Papers 2010-10, Bar-Ilan University, Department of Economics.
- 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..
- 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 175-86, February.
- Karotkin, Drora, 1994. "Effect of the size of the bench on the correctness of court judgments: The case of Israel," International Review of Law and Economics, Elsevier, vol. 14(3), pages 371-375, September.
- 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.
- Daniel Berend & Luba Sapir, 2005. "Monotonicity in Condorcet Jury Theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 83-92, 08.
- Lloyd Shapley & Bernard Grofman, 1984. "Optimizing group judgmental accuracy in the presence of interdependencies," Public Choice, Springer, vol. 43(3), pages 329-343, January.
- Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
- Leonid V. Azarnert, 2008. "Involuntary Integration in Public Education, Fertility and Human Capital," Working Papers 2008-07, Bar-Ilan University, Department of Economics.
- Ruth Ben-Yashar & Igal Milchtaich, 2007. "First and second best voting rules in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 453-486, October.
- Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:72:y:2012:i:1:p:113-130. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Rebekah McClure)
If references are entirely missing, you can add them using this form.