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On Small Coalitions, Hierarchic Decision Making and Collective Competence

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Power Indices and Coalition Formation

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.

The author is grateful for finacial support from the Swedish Council for Research in the Humanities and Social Sciences and for valuable comments from one of the editors.

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References

  • Berg, S. (1993), “Condorcet’s Jury Theorem, Dependency Among Voters”, Social Choice and Welfare, 10, 87–96.

    Article  Google Scholar 

  • Berg, S. (1997), “Indirect Voting Systems: Banzhaf Numbers, Majority Functions and Collective Competence’, European Journal of Political Economy, 13, 557–573.

    Article  Google Scholar 

  • Berg, S., and J. Paroush (1998), “Collective decision making in hierarchies”, Mathematical Social Sciences, 35, 233–244.

    Article  Google Scholar 

  • Boland, P.J. (1989), “Majority systems and the Condorcet Jury Theorem”, The Statistician, 38, 181–189.

    Article  Google Scholar 

  • Boland, P.J., F. Proschan, and Y.L. Tong (1989), “Modelling Dependence in Simple and Indirect Majority Systems”, Appl. Prob., 26, 81–88.

    Article  Google Scholar 

  • Fishburn, P.C. (1973), The Theory of Social Choice, Princeton, New Jersey: Princeton University Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Fishburn, P.C., and S.J. Brams (1995), “Minimal winning coalitions in weighted-majority voting games”, Working paper, 1–30.

    Google Scholar 

  • Holler, M., and E. Packel (1983), “Power, luck and the right index”, Zeitschrift far Nationalökonomie, 43, 21–29.

    Article  Google Scholar 

  • Kelly, J.S. (1984), “Simple majority voting isn’t special”, Mathematical Social Sciences, 7, 13–20.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Nitzan S., and J. Paroush (1982), “Optimal decision rules in uncertain dichotomous choice situations”, International Economic Review, 23, 289–297.

    Article  Google Scholar 

  • Owen, G. (1972), “Multilinear extensions of games”, Management Science, 18, 64–79.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Shapley, L., and B. Grofman (1984), “Optimizing group judgmental accuracy in the presence of interdependence”, Public Choice, 43, 329–343.

    Article  Google Scholar 

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© 2001 Springer Science+Business Media New York

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Berg, S. (2001). On Small Coalitions, Hierarchic Decision Making and Collective Competence. In: Holler, M.J., Owen, G. (eds) Power Indices and Coalition Formation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6221-1_12

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  • DOI: https://doi.org/10.1007/978-1-4757-6221-1_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4893-9

  • Online ISBN: 978-1-4757-6221-1

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