Abstract
This study identifies the optimal collective decision rule in a dichotomous symmetric setting, allowing for probabilities distortion as originally assumed by Tversky and Kahneman (Journal of Risk and Uncertainty 5(4):297–323, 1992). We show that previous results that identified the weighted majority rule as the optimal one, and did not consider subjective probabilities, are robust to such distortion in the sense that neither the rule nor the weights are changed.
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References
Arrow, K. J. (1951). Individual values and social choice. New York: Wiley.
Ben-Yashar, R. (2006). Information is important to Condorcet jurors. Public Choice, 127, 313–27.
Ben-Yashar, R., & Kraus, S. (2002). Optimal collective dichotomous choice under quota constraints. Economic Theory, 19(4), 839–52.
Ben-Yashar, R., & Nitzan, S. (1997). The optimal decision rule for fixed-size committees in dichotomous choice situations: the general result. International Economic Review, 38(1), 175–86.
Ben-Yashar, R., & Nitzan, S. (2001). Investment criteria in single- and multi-member economic organizations. Public Choice, 109, 1–13.
Ben-Yashar, R., & Paroush, J. (2000). A nonasymptotic Condorcet jury theorem. Social Choice and Welfare, 17, 189–99.
Ben-Yashar, R., & Paroush, J. (2001). Optimal decision rules for fixed-size committees in polychotomous choice. Social Choice and Welfare, 18(4), 737–46.
Buchanan, J. M., & Tullock, G. (1962). The calculus of consent. Ann Arbor: University of Michigan Press.
Camerer, C. F., & Ho, T. H. (1994). Violations of the betweenness axiom and nonlinearity in probability. Journal of Risk and Uncertainty, 8, 167–96.
de Condorcet, N. C. (1785). Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. Paris. Translated by I. McLean and F. Hewitt (1994).
Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263–91.
Nitzan, S., & Paroush, J. (1981). The characterization of decisive weighted majority rules. Economics Letters, 7, 119–124.
Nitzan, S., & Paroush, J. (1982). Optimal decision rules in uncertain dichotomous choice situations. International Economic Review, 23(2), 289–97.
Nitzan, S., & Paroush, J. (1984). Are qualified majority rules special? Public Choice, 42, 257–72.
Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497–527.
Quiggin, J. (1991). Comparative statics for rank-dependent expected utility theory. Journal of Risk and Uncertainty, 4(4), 339–50.
Rae, D. W. (1969). Decision rules and individual values in constitutional choice. American Political Science Review, 63, 40–56.
Sah, R. K. (1991). Fallibility in human organizations and political systems. The Journal of Economic Perspectives, 5, 67–88.
Sah, R. K., & Stiglitz, J. E. (1985). The theory of economic organizations, human fallibility and economic organizations. American Economic Review, Papers and Proceedings, 75, 292–97.
Sah, R. K., & Stiglitz, J. E. (1986). The architecture of economic systems: hierarchies and polyarchies. American Economic Review, 76, 716–27.
Sah, R. K., & Stiglitz, J. E. (1988). Committees, hierarchies and polyarchies. The Economic Journal, 98, 451–70.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.
Tversky, A., & Wakker, P. (1995). Risk attitudes and decision weights. Econometrica, 63(6), 1255–1280.
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We thank Doron Kliger, Shmuel Nitzan, Jacob Paroush, the editor, and two anonymous referees for their useful comments and discussions. The second author acknowledges the support of the Schnitzer Foundation for Research on the Israeli Economy and Society.
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Baharad, E., Ben-Yashar, R. The robustness of the optimal weighted majority rule to probability distortion. Public Choice 139, 53–59 (2009). https://doi.org/10.1007/s11127-008-9378-7
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DOI: https://doi.org/10.1007/s11127-008-9378-7