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Axiomatizations of a Positional Power Score and Measure for Hierarchies

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  • René van den Brink

    ()
    (VU University Amsterdam)

  • Frank Steffen

    ()
    (The University of Liverpool and University of Hamburg)

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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-115/1.

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Date of creation: 24 Nov 2008
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Handle: RePEc:dgr:uvatin:20080115

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Keywords: hierarchies; decision-making mechanism; power; positional power; power score; power measure; binary voting; axiomatization;

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References

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  1. René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer, Springer, vol. 30(3), pages 309-319.
  2. Matthias Sutter, 2000. "Flexible Integration, EMU and Relative Voting Power in the EU," Public Choice, Springer, Springer, vol. 104(1), pages 41-62, July.
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  10. Felsenthal, Dan S & Machover, Moshe, 1996. " Alternative Forms of the Shapley Value and the Shapley-Shubik Index," Public Choice, Springer, Springer, vol. 87(3-4), pages 315-18, June.
  11. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, Springer, vol. 15(4), pages 567-582.
  12. René Brink, 2008. "Vertical wage differences in hierarchically structured firms," Social Choice and Welfare, Springer, Springer, vol. 30(2), pages 225-243, February.
  13. Lloyd S. Shapley & Jorge R. Palamara, 2000. "Simple Games and Authority Structure," UCLA Economics Working Papers, UCLA Department of Economics 796, UCLA Department of Economics.
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  17. Leech, Dennis, 2002. " Designing the Voting System for the Council of the European Union," Public Choice, Springer, Springer, vol. 113(3-4), pages 437-64, December.
  18. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 12(1), pages 113-126, January.
  19. RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, Springer, vol. 26(1), pages 27-43.
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  21. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, Springer, vol. 20(3), pages 277-93.
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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, Tinbergen Institute 12-030/1, Tinbergen Institute.
  2. Ren� van den Brink & Frank Steffen, 2012. "On the Measurement of Success and Satisfaction," Tinbergen Institute Discussion Papers, Tinbergen Institute 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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