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Axiomatizations of a positional power score and measure for hierarchies

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  • René Brink

    ()

  • Frank Steffen

    ()

Abstract

Power is a core concept in the analysis and design of organizations. One of the problems with the extant literature on positional power in hierarchies is that it is mainly restricted to the analysis of power in terms of the bare positions of the actors. While such an analysis informs us about the authority structure within an organization, it ignores the decision-making mechanisms completely. The few studies which take into account the decision-making mechanisms make all use of adaptations of well-established approaches for the analysis of power in non-hierarchical organizations such as the Banzhaf measure; and thus they are all based on the structure of a simple game, i.e. they are `membership-based'. In van den Brink and Steffen (2008) it is demonstrated that such an approach is in general inappropriate for characterizing power in hierarchies as it cannot be extended to a class of decision-making mechanisms which allow certain actors to terminate a decision before all other members have been involved. As this kind of sequential decision-making mechanism turns out to be particularly relevant for hierarchies, we suggested an action-based approach - represented by an extensive game form - which can take the features of such mechanisms into account. Based on this approach we introduced a power score and power measure that can be applied to ascribe positional power to actors in sequential decision making mechanisms. In this paper we provide axiomatizations of this power score and power measure for one of the most studied decision models, namely that of binary voting.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by Springer in its journal Public Choice.

Volume (Year): 151 (2012)
Issue (Month): 3 (June)
Pages: 757-787

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Handle: RePEc:kap:pubcho:v:151:y:2012:i:3:p:757-787

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Web page: http://www.springerlink.com/link.asp?id=100332

Related research

Keywords: Hierarchies; Decision-making mechanism; Power; Positional power; Power score; Power measure; Binary voting; Axiomatization; C79; D02; D71;

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References

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  1. Felsenthal, Dan S & Machover, Moshe, 1996. " Alternative Forms of the Shapley Value and the Shapley-Shubik Index," Public Choice, Springer, vol. 87(3-4), pages 315-18, June.
  2. Fischer, A J, 1999. " The Probability of Being Decisive," Public Choice, Springer, vol. 101(3-4), pages 267-83, December.
  3. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, vol. 20(3), pages 277-93.
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  6. RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, vol. 26(1), pages 27-43.
  7. Lloyd S. Shapley & Jorge R. Palamara, 2000. "Simple Games and Authority Structure," UCLA Economics Working Papers 796, UCLA Department of Economics.
  8. Chwe, Michael Suk-Young, 2000. "Communication and Coordination in Social Networks," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 1-16, January.
  9. René van den Brink & Frank Steffen, 2007. "Positional Power in Hierarchies," Tinbergen Institute Discussion Papers 07-038/1, Tinbergen Institute.
  10. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
  11. Mathias Dewatripont & Patrick Bolton, 1994. "The firm as a communication network," ULB Institutional Repository 2013/9595, ULB -- Universite Libre de Bruxelles.
  12. Leech, Dennis, 2002. " Designing the Voting System for the Council of the European Union," Public Choice, Springer, vol. 113(3-4), pages 437-64, December.
  13. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, vol. 24(3), pages 439-454, 06.
  14. René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer, vol. 30(3), pages 309-319.
  15. Matthias Sutter, 2000. "Flexible Integration, EMU and Relative Voting Power in the EU," Public Choice, Springer, vol. 104(1), pages 41-62, July.
  16. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
  17. Stefan Napel & Mika Widgrén, 2006. "The Inter-Institutional Distribution of Power in EU Codecision," Social Choice and Welfare, Springer, vol. 27(1), pages 129-154, August.
  18. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, October.
  19. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, vol. 15(4), pages 567-582.
  20. Oliver E. Williamson, 1967. "Hierarchical Control and Optimum Firm Size," Journal of Political Economy, University of Chicago Press, vol. 75, pages 123.
  21. Lloyd S. Shapley & Jorge R. Palamara, 2000. "Control Games and Organizations," UCLA Economics Working Papers 795, UCLA Department of Economics.
  22. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
  23. Berg, Sven & Paroush, Jacob, 1998. "Collective decision making in hierarchies," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 233-244, May.
  24. Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Discussion Paper 1999-20, Tilburg University, Center for Economic Research.
  25. René Brink, 2008. "Vertical wage differences in hierarchically structured firms," Social Choice and Welfare, Springer, vol. 30(2), pages 225-243, February.
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Citations

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Cited by:
  1. Ren� van den Brink & Frank Steffen, 2012. "On the Measurement of Success and Satisfaction," Tinbergen Institute Discussion Papers 12-030/1, Tinbergen Institute.
  2. Ren� van den Brink & Frank Steffen, 2012. "On the Measurement of Success and Satisfaction," Tinbergen Institute Discussion Papers 12-030/1, Tinbergen Institute.
  3. Yucel, Eray & Tokel, Emre, 2010. "Fibonacci Hierarchies for Decision Making," MPRA Paper 20973, University Library of Munich, Germany.

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