Advertisement

On Small Coalitions, Hierarchic Decision Making and Collective Competence

  • Sven Berg
Chapter

Abstract

This paper discusses the reliability of group judgment in the context of decentralized decision making systems (indirect voting). Composite majority functions are introduced and their properties studied along with coalition structures. The effects on collective competence of grouping individuals in a hierarchic system are examined. Formulas are developed to measure the loss (or gain) in judgmental competence.

Keywords

Social Choice Majority Function Power Index Coalition Formation Coalition Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berg, S. (1993), “Condorcet’s Jury Theorem, Dependency Among Voters”, Social Choice and Welfare, 10, 87–96.CrossRefGoogle Scholar
  2. Berg, S. (1997), “Indirect Voting Systems: Banzhaf Numbers, Majority Functions and Collective Competence’, European Journal of Political Economy, 13, 557–573.CrossRefGoogle Scholar
  3. Berg, S., and J. Paroush (1998), “Collective decision making in hierarchies”, Mathematical Social Sciences, 35, 233–244.CrossRefGoogle Scholar
  4. Boland, P.J. (1989), “Majority systems and the Condorcet Jury Theorem”, The Statistician, 38, 181–189.CrossRefGoogle Scholar
  5. Boland, P.J., F. Proschan, and Y.L. Tong (1989), “Modelling Dependence in Simple and Indirect Majority Systems”, Appl. Prob., 26, 81–88.CrossRefGoogle Scholar
  6. Fishburn, P.C. (1973), The Theory of Social Choice, Princeton, New Jersey: Princeton University Press.Google Scholar
  7. Fishburn, P.C., and W.V. Gehrlein (1977), “Collective rationality versus distribution of power of binary social choice functions”, Journal of Economic Theory, 16, 72–91.CrossRefGoogle Scholar
  8. Fishburn, P.C., and S.J. Brams (1995), “Minimal winning coalitions in weighted-majority voting games”, Working paper, 1–30.Google Scholar
  9. Holler, M., and E. Packel (1983), “Power, luck and the right index”, Zeitschrift far Nationalökonomie, 43, 21–29.CrossRefGoogle Scholar
  10. Kelly, J.S. (1984), “Simple majority voting isn’t special”, Mathematical Social Sciences, 7, 13–20.CrossRefGoogle Scholar
  11. Ladha, K.K. (1993), “Condorcet’s jury theorem in light of de Finetti’s theorem. Majority voting with correlated votes”, Social Choice and Welfare, 10, 69–86.CrossRefGoogle Scholar
  12. Nitzan S., and J. Paroush (1982), “Optimal decision rules in uncertain dichotomous choice situations”, International Economic Review, 23, 289–297.CrossRefGoogle Scholar
  13. Owen, G. (1972), “Multilinear extensions of games”, Management Science, 18, 64–79.CrossRefGoogle Scholar
  14. Owen, G., B. Grofman, and S.L. Feld (1989), “Proving a distribution-free generalization of the Condorcet jury theorem”, Mathematical Social Sciences, 17, 1–16.CrossRefGoogle Scholar
  15. Shapley, L., and B. Grofman (1984), “Optimizing group judgmental accuracy in the presence of interdependence”, Public Choice, 43, 329–343.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Sven Berg
    • 1
  1. 1.Department of StatisticsUniversity of LundLundSweden

Personalised recommendations