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Are two better than one? A note

Author

Listed:
  • Ruth Ben-Yashar

    (Bar Ilan University)

  • Shmuel Nitzan

    (Bar Ilan University)

Abstract

This note examines the possibility of extending the Condorcet Jury Theorem (CJT) by relaxing the assumption of homogeneous individual decision-making skills. Our main result provides two sufficient conditions for advantageous extension of a group. These conditions are referred to as (Weak) “Two Are Better than One” (WTBO) and TBO. The latter requires that the average decision-making competence of the two added members exceeds those of any existing group member. The weaker condition WTBO requires that the sum of the optimal weights of the two added members is larger than the optimal weight of any existing group member. Immediate special cases of our result include CJT settings wherein decision-making skills are assumed to be identical as well as situations wherein such skills are of two types: low and high.

Suggested Citation

  • Ruth Ben-Yashar & Shmuel Nitzan, 2017. "Are two better than one? A note," Public Choice, Springer, vol. 171(3), pages 323-329, June.
    • Handle: RePEc:kap:pubcho:v:171:y:2017:i:3:d:10.1007_s11127-017-0439-7
    DOI: 10.1007/s11127-017-0439-7
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    References listed on IDEAS

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    1. Ruth Ben-Yashar & Shmuel Nitzan, 2014. "On the significance of the prior of a correct decision in committees," Theory and Decision, Springer, vol. 76(3), pages 317-327, March.
    2. Drora Karotkin & Jacob Paroush, 2003. "Optimum committee size: Quality-versus-quantity dilemma," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 429-441, June.
    3. Ladha, Krishna K., 1995. "Information pooling through majority-rule voting: Condorcet's jury theorem with correlated votes," Journal of Economic Behavior & Organization, Elsevier, vol. 26(3), pages 353-372, May.
    4. Ben-Yashar, Ruth & Danziger, Leif, 2011. "Symmetric and asymmetric committees," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 440-447.
    5. Ruth Ben-Yashar & Mor Zahavi, 2011. "The Condorcet jury theorem and extension of the franchise with rationally ignorant voters," Public Choice, Springer, vol. 148(3), pages 435-443, September.
    6. Ruth Ben-Yashar, 2014. "The generalized homogeneity assumption and the Condorcet jury theorem," Theory and Decision, Springer, vol. 77(2), pages 237-241, August.
    7. Ruth Ben-Yashar & Jacob Paroush, 2000. "A nonasymptotic Condorcet jury theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 189-199.
    8. 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.
    9. Kanazawa, Satoshi, 1998. "A brief note on a further refinement of the Condorcet Jury Theorem for heterogeneous groups," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 69-73, January.
    10. Scott Feld & Bernard Grofman, 1984. "The accuracy of group majority decisions in groups with added members," Public Choice, Springer, vol. 42(3), pages 273-285, January.
    11. Lloyd Shapley & Bernard Grofman, 1984. "Optimizing group judgmental accuracy in the presence of interdependencies," Public Choice, Springer, vol. 43(3), pages 329-343, January.
    12. 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.
    13. 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.
    14. Eyal Baharad & Ruth Ben-Yashar, 2009. "The robustness of the optimal weighted majority rule to probability distortion," Public Choice, Springer, vol. 139(1), pages 53-59, April.
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    1. Ronen Bar-El & Mordechai E. Schwarz, 2021. "A Talmudic constrained voting majority rule," Public Choice, Springer, vol. 189(3), pages 465-491, December.

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