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Constrained Monotonicity and the Measurement of Power

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  • Manfred Holler
  • Rie Ono
  • Frank Steffen

Abstract

In this paper we will discuss constraints on the number of (non-dummy) players and on the distribution of votes such that local monotonicity is satisfied for the Public Good Index. These results are compared to properties which are related to constraints on the redistribution of votes (such as implied by global monotonicity). The discussion shows that monotonicity is not a straightforward criterion of classification for power measures. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Manfred Holler & Rie Ono & Frank Steffen, 2001. "Constrained Monotonicity and the Measurement of Power," Theory and Decision, Springer, vol. 50(4), pages 383-395, June.
    • Handle: RePEc:kap:theord:v:50:y:2001:i:4:p:383-395
    DOI: 10.1023/A:1010335410952
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    References listed on IDEAS

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    1. Turnovec, Frantisek, 1997. "Monotonicity of Power Indices," East European Series 41, Institute for Advanced Studies.
    2. Steven J. Brams & Peter C. Fishburn, 1996. "Minimal winning coalitions in weighted-majority voting games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(4), pages 397-417.
    3. Dan Felsenthal & Moshé Machover & William Zwicker, 1998. "The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision, Springer, vol. 44(1), pages 83-116, January.
    4. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    5. MoshÚ Machover, 2000. "Notions of A Priori Voting Power: Critique of Holler and WidgrÚn," Homo Oeconomicus, Institute of SocioEconomics, vol. 16, pages 415-425.
    6. Stefan Napel, 1999. "The Holler-Packel Axiomatization of the Public Good Index Completed," Homo Oeconomicus, Institute of SocioEconomics, vol. 15, pages 513-520.
    7. Steven J. Brams & Peter C. Fishburn, 1995. "When is Size a Liability?," Journal of Theoretical Politics, , vol. 7(3), pages 301-316, July.
    8. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    Cited by:

    1. Freixas, Josep & Kurz, Sascha, 2016. "The cost of getting local monotonicity," European Journal of Operational Research, Elsevier, vol. 251(2), pages 600-612.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

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