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Monotonicity of power and power measures

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  • Manfred Holler

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  • Stefan Napel

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Abstract

Monotonicity is commonly considered an essential requirement for power measures; violation of local monotonicity or related postulates supposedly disqualifies an index as a valid yardstick for measuring power. This paper questions if such claims are really warranted. In the light of features of real-world collective decision making such as coalition formation processes, ideological affinities, a priori unions, and strategic interaction, standard notions of monotonicity are too narrowly defined. A power measure should be able to indicate that power is non-monotonic in a given dimension of players’ resources if – given a decision environment and plausible assumptions about behaviour – itis non-monotonic. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Manfred Holler & Stefan Napel, 2004. "Monotonicity of power and power measures," Theory and Decision, Springer, vol. 56(1), pages 93-111, April.
  • Handle: RePEc:kap:theord:v:56:y:2004:i:1:p:93-111
    DOI: 10.1007/s11238-004-5638-2
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    File URL: http://hdl.handle.net/10.1007/s11238-004-5638-2
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    References listed on IDEAS

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    1. Steven Brams & Michael Jones & D. Kilgour, 2005. "Forming stable coalitions: The process matters," Public Choice, Springer, vol. 125(1), pages 67-94, July.
    2. Napel,S. & Widgren,M., 2002. "Power measurement as sensitivity analysis : a unified approach," Center for Mathematical Economics Working Papers 345, Center for Mathematical Economics, Bielefeld University.
    3. Manfred Holler & Stefan Napel, 2005. "Local monotonicity of power: Axiom or just a property?," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(5), pages 637-647, January.
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    Cited by:

    1. Alpern, Steve & Gal, Shmuel & Solan, Eilon, 2010. "A sequential selection game with vetoes," Games and Economic Behavior, Elsevier, vol. 68(1), pages 1-14, January.
    2. Geller, Chris R. & Mustard, Jamie & Shahwan, Ranya, 2013. "Focused power: Experiments, the Shapley-Shubik power index, and focal points," Economics Discussion Papers 2013-42, Kiel Institute for the World Economy (IfW).
    3. Freixas, Josep & Kurz, Sascha, 2016. "The cost of getting local monotonicity," European Journal of Operational Research, Elsevier, vol. 251(2), pages 600-612.
    4. Maria Montero & Juan Vidal-Puga, 2012. "A Violation of Monotonicity in a Noncooperative Setting," Discussion Papers 2012-04, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    5. J. Alonso-Meijide & C. Bowles & M. Holler & S. Napel, 2009. "Monotonicity of power in games with a priori unions," Theory and Decision, Springer, vol. 66(1), pages 17-37, January.
    6. Napel, Stefan & Nohn, Andreas & Alonso-Meijide, José Maria, 2012. "Monotonicity of power in weighted voting games with restricted communication," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 247-257.
    7. Dan S. Felsenthal, 2016. "A Well-Behaved Index of a Priori P-Power for Simple N-Person Games," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(4), pages 367-381, December.

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    Keywords

    Power measures; monotonicity; voting;

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