Public Choice

, Volume 171, Issue 3–4, pp 323–329 | Cite as

Are two better than one? A note



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.


  1. Baharad, E., & Ben-Yashar, R. (2009). The robustness of the optimal weighted majority rule to probabilities distortion. Public Choice, 139, 53–59.CrossRefGoogle Scholar
  2. Ben-Yashar, R. (2014). The generalized homogeneity assumption and the Condorcet Jury Theorem. Theory and Decision, 77, 237–241.CrossRefGoogle Scholar
  3. Ben-Yashar, R., & Danziger, L. (2011). Symmetric and asymmetric committees. Journal of Mathematical Economics, 47, 440–447.CrossRefGoogle Scholar
  4. Ben-Yashar, R., & Nitzan, S. (2014). On the significance of the prior of a correct decision in committees. Theory and Decision, 76, 317–327.CrossRefGoogle Scholar
  5. Ben-Yashar, R., & Paroush, J. (2000). A nonasymptotic Condorcet Jury Theorem. Social Choice and Welfare, 17, 189–199.CrossRefGoogle Scholar
  6. Ben-Yashar, R., & Zahavi, M. (2011). The Condorcet Jury Theorem and extension of the franchise with rationally ignorant voters. Public Choice, 48, 435–443.CrossRefGoogle Scholar
  7. Berend, D., & Paroush, J. (1998). When is Condorcet’s Jury Theorem valid? Social Choice and Welfare, 15, 481–488.CrossRefGoogle Scholar
  8. Berend, D., & Sapir, L. (2005). Monotonicity in Condorcet Jury Theorem. Social Choice and Welfare, 24, 83–92.CrossRefGoogle Scholar
  9. Condorcet, N.C. de. (1785). Essai sur l’Application de l’Analyse à la Probabilité des Décisions Rendues à la Pluralité des Voix, Paris. (trans: McLean, I., Hewitt, F.) 1994.Google Scholar
  10. Dietrich, F., & List, C. (2013). Propositionwise judgment aggregation: The general case. Social Choice and Welfare, 40, 1067–1095.CrossRefGoogle Scholar
  11. Feld, S. L., & Grofman, B. (1984). The accuracy of group majority decisions in groups with added members. Public Choice, 42, 273–285.CrossRefGoogle Scholar
  12. Grofman, B., Owen, G., & Feld, S. L. (1983). Thirteen theorems in search of truth. Theory and Decision, 15, 261–278.CrossRefGoogle Scholar
  13. Hoeffding, W. (1956). On the distribution of successes in independent trials. The Annals of Mathematical Statistics, 27, 713–721.CrossRefGoogle Scholar
  14. Kanazawa, S. (1998). A brief note on a future refinement of the Condorcet Jury Theorem for heterogeneous groups. Mathematical Social Sciences, 35, 69–73.CrossRefGoogle Scholar
  15. Karotkin, D., & Paroush, J. (2003). Optimum committee size: Quality-versus-quantity dilemma. Social Choice and Welfare, 20, 429–441.CrossRefGoogle Scholar
  16. Ladha, K. K. (1995). Information pooling through majority-rule voting: Condorcet’s Jury Theorem with correlated votes. Journal of Economic Behavior & Organization, 26, 353–372.CrossRefGoogle Scholar
  17. Miller, N. R. (1986). Information electorates and democracy: Some extensions and interpretation of the Condorcet Jury Theorem. In B. Grofman & G. Owen (Eds.), Information pooling and group decision making. Greenwich, CT: JAI Press.Google Scholar
  18. Nitzan, S., & Paroush, J. (1982). Optimal decision rules in uncertain dichotomous choice situation. International Economic Review, 23, 289–297.CrossRefGoogle Scholar
  19. Nitzan, S., & Paroush, J. (2017). Collective decision making and jury theorems. In F. Persico (Eds.), Oxford handbook of law and economics. Oxford: Oxford University Press.Google Scholar
  20. Owen, G. B., Grofman, B., & Feld, S. L. (1989). Proving a distribution-free generalization of the Condorcet Jury Theorem. Mathematical Social Sciences, 17, 1–16.CrossRefGoogle Scholar
  21. Shapley, L., & Grofman, B. (1984). Optimizing group judgmental accuracy in the presence of interdependencies. Public Choice, 43, 329–343.CrossRefGoogle Scholar
  22. Young, H. P. (1988). Condorcet’s theory of voting. American Political Science Review, 82, 1231–1244.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of EconomicsBar Ilan UniversityRamat GanIsrael

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