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Monotonicity of power and power measures

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  • Manfred J. Holler
  • Stefan Napel

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
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  • Manfred J. Holler & Stefan Napel, 2004. "Monotonicity of power and power measures," Theory and Decision, Springer, vol. 56(2_2), pages 93-111, February.
    • Handle: RePEc:kap:theord:v:56:y:2004:i:2_2:p:93-111
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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, Stefan & Widgrén, Mika, 2017. "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.
    4. Stefan Napel & Mika Widgren, 2004. "Power Measurement as Sensitivity Analysis," Journal of Theoretical Politics, , vol. 16(4), pages 517-538, October.
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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. 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.
    3. Fuad Aleskerov & Manfred Holler & Rita Kamalova, 2014. "Power distribution in the Weimar Reichstag in 1919–1933," Annals of Operations Research, Springer, vol. 215(1), pages 25-37, April.
    4. 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.
    5. Hannu Nurmi, 2010. "Voting Weights or Agenda Control: Which One Really Matters?," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 4(1), pages 005-017, March.
    6. Katrin Zulauf & Ralf Wagner, 2023. "Countering Negotiation Power Asymmetries by Using the Adjusted Winner Algorithm," SN Operations Research Forum, Springer, vol. 4(1), pages 1-20, March.
    7. 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 Kiel).
    8. Freixas, Josep & Kurz, Sascha, 2016. "The cost of getting local monotonicity," European Journal of Operational Research, Elsevier, vol. 251(2), pages 600-612.
    9. 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.
    10. José María Alonso‐Meijide & Manfred J. Holler, 2009. "Freedom Of Choice And Weighted Monotonicity Of Power," Metroeconomica, Wiley Blackwell, vol. 60(4), pages 571-583, November.
    11. Josep Freixas & Roberto Lucchetti, 2016. "Power in voting rules with abstention: an axiomatization of a two components power index," Annals of Operations Research, Springer, vol. 244(2), pages 455-474, September.
    12. 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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