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Inequality of decision-makers’ power and marginal contribution

Author

Listed:
  • Shmuel Nitzan

    (Bar Ilan University)

  • Tomoya Tajika

    (Hokusei Gakuen University)

Abstract

Modest difference in individual decisional skills may warrant substantial inequality in power. This claim has been illustrated in Ben Yashar and Nitzan (Economics Letters 174:93–95, 2019), applying the symmetric uncertain dichotomous choice setting and focusing on the skill-dependent (s-d) power of the decision-makers under the optimal decision rule. The same claim is valid when one focuses on the relationship between skill heterogeneity and the distribution of the second type of power, viz., the group members' marginal contribution (mc). This has been shown in Ben Yashar et al. (Journal of Theoretical Politics 33(2):225–235, 2021), where mc has been formally related to s-d power. A preliminary study of the relationship between inequality of the distributions of the two measures has also been presented. The current paper considerably expands this investigation by applying simulations and sheds light on the reason for the increased inequality of the two types of power. Since reward (in terms of status, payment or both) depends on s-d power and mc, inequality of the distribution of rewards depends on the inequality of the two types of power. Comparison of the two types of power inequality is therefore interesting if one wishes to shed light on the role of the two types of power on reward inequality. In particular, the results of the comparison may clarify the effectiveness of the incentives to invest in skills, dependent on the prevailing norms and the institutional characteristics that determine the relationship between rewards and the two types of power. For this reason, the current study focuses on the comparison between inequality of s-d power and marginal contributions showing that, in small (large) groups, on average, the latter is more (less) unequal than the former and both are more unequal than the optimal weights of the decision-makers and much more unequal than their skills. The robustness of these findings is shown by applying alternative symmetric probability distribution functions. Another novel task undertaken in the current study is the sensitivity analysis of inequality of the power measures with respect to changes in the size of the group and the skills of the group members.

Suggested Citation

  • Shmuel Nitzan & Tomoya Tajika, 2022. "Inequality of decision-makers’ power and marginal contribution," Theory and Decision, Springer, vol. 92(2), pages 275-292, March.
    • Handle: RePEc:kap:theord:v:92:y:2022:i:2:d:10.1007_s11238-021-09816-1
    DOI: 10.1007/s11238-021-09816-1
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    References listed on IDEAS

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    1. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, vol. 65(5), pages 1029-1058, September.
    2. Franz Dietrich & Christian List, 2013. "Propositionwise judgment aggregation: the general case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1067-1095, April.
    3. Lloyd Shapley & Bernard Grofman, 1984. "Optimizing group judgmental accuracy in the presence of interdependencies," Public Choice, Springer, vol. 43(3), pages 329-343, January.
    4. 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.
    5. Austen-Smith, David & Banks, Jeffrey S., 1996. "Information Aggregation, Rationality, and the Condorcet Jury Theorem," American Political Science Review, Cambridge University Press, vol. 90(1), pages 34-45, March.
    6. 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.
    7. Ben-Yashar, Ruth & Nitzan, Shmuel, 2019. "Skill, value and remuneration in committees," Economics Letters, Elsevier, vol. 174(C), pages 93-95.
    8. Eyal Baharad & Jacob Goldberger & Moshe Koppel & Shmuel Nitzan, 2012. "Beyond Condorcet: optimal aggregation rules using voting records," Theory and Decision, Springer, vol. 72(1), pages 113-130, January.
    9. Ruth Ben-Yashar & Shmuel Nitzan & Tomoya Tajika, 2021. "Skill, power and marginal contribution in committees," Journal of Theoretical Politics, , vol. 33(2), pages 225-235, April.
    10. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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