IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v251y2016i2p600-612.html
   My bibliography  Save this article

The cost of getting local monotonicity

Author

Listed:
  • Freixas, Josep
  • Kurz, Sascha

Abstract

Committees with yes-no-decisions are commonly modeled as simple games and the ability of a member to influence the group decision is measured by so-called power indices. For a weighted game we say that a power index satisfies local monotonicity if a player who controls a large share of the total weight vote does not have less power than a player with a smaller voting weight.

Suggested Citation

  • Freixas, Josep & Kurz, Sascha, 2016. "The cost of getting local monotonicity," European Journal of Operational Research, Elsevier, vol. 251(2), pages 600-612.
    • Handle: RePEc:eee:ejores:v:251:y:2016:i:2:p:600-612
    DOI: 10.1016/j.ejor.2015.11.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715010796
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.11.030?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sascha Kurz, 2012. "On minimum sum representations for weighted voting games," Annals of Operations Research, Springer, vol. 196(1), pages 361-369, July.
    2. Freixas, Josep & Puente, Maria Albina, 2008. "Dimension of complete simple games with minimum," European Journal of Operational Research, Elsevier, vol. 188(2), pages 555-568, July.
    3. Manfred J. Holler & Stefan Napel, 2004. "Monotonicity of power and power measures," Theory and Decision, Springer, vol. 56(2_2), pages 93-111, February.
    4. Algaba, E. & Bilbao, J.M. & Fernandez, J.R., 2007. "The distribution of power in the European Constitution," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1752-1766, February.
    5. Bilbao, J. M. & Fernandez, J. R. & Jimenez, N. & Lopez, J. J., 2002. "Voting power in the European Union enlargement," European Journal of Operational Research, Elsevier, vol. 143(1), pages 181-196, November.
    6. Freixas, Josep & Marciniak, Dorota & Pons, Montserrat, 2012. "On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 367-375.
    7. Sascha Kurz & Stefan Napel, 2014. "Heuristic and exact solutions to the inverse power index problem for small voting bodies," Annals of Operations Research, Springer, vol. 215(1), pages 137-163, April.
    8. Widgren, Mika, 1994. "Voting power in the EC decision making and the consequences of two different enlargements," European Economic Review, Elsevier, vol. 38(5), pages 1153-1170, May.
    9. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    10. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    11. 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.
    12. R J Johnston, 1978. "On the Measurement of Power: Some Reactions to Laver," Environment and Planning A, , vol. 10(8), pages 907-914, August.
    13. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 411-437, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Josep Freixas & Montserrat Pons, 2022. "A critical analysis on the notion of power," Annals of Operations Research, Springer, vol. 318(2), pages 911-933, November.
    2. Kong, Qianqian & Peters, Hans, 2023. "Power indices for networks, with applications to matching markets," European Journal of Operational Research, Elsevier, vol. 306(1), pages 448-456.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    2. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    3. Josep Freixas & Sascha Kurz, 2014. "Enumeration of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum," Annals of Operations Research, Springer, vol. 222(1), pages 317-339, November.
    4. Freixas, Josep & Kurz, Sascha, 2013. "The golden number and Fibonacci sequences in the design of voting structures," European Journal of Operational Research, Elsevier, vol. 226(2), pages 246-257.
    5. D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2023. "Voting power in the Council of the European Union: A comprehensive sensitivity analysis," Papers 2312.16878, arXiv.org, revised Sep 2024.
    6. Sascha Kurz, 2016. "The inverse problem for power distributions in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 65-88, June.
    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.
    8. Josep Freixas & Marc Freixas & Sascha Kurz, 2017. "On the characterization of weighted simple games," Theory and Decision, Springer, vol. 83(4), pages 469-498, December.
    9. 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.
    10. Josep Freixas & Montserrat Pons, 2017. "Using the Multilinear Extension to Study Some Probabilistic Power Indices," Group Decision and Negotiation, Springer, vol. 26(3), pages 437-452, May.
    11. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    12. Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.
    13. Leech, Dennis, 2002. "The Use Of Coleman'S Power Indices To Inform The Choice Of Voting Rule With Reference To The Imf Governing Body And The Eu Council Of Ministers," The Warwick Economics Research Paper Series (TWERPS) 645, University of Warwick, Department of Economics.
    14. Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00142479, HAL.
      • Agnieszka Rusinowska & Michel Grabisch, 2007. "Influence Indices," Working Papers 0705, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
      • Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," Post-Print halshs-00142479, HAL.
    15. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    16. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali, 2006. "On the Coleman indices of voting power," European Journal of Operational Research, Elsevier, vol. 171(1), pages 273-289, May.
    17. 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).
    18. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    19. Freixas, Josep & Kurz, Sascha, 2014. "On minimum integer representations of weighted games," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 9-22.
    20. Borkowski, Agnieszka, 2003. "Machtverteilung im Ministerrat: nach dem Vertrag von Nizza und den Konventsvorschlägen in einer erweiterten Europäischen Union," IAMO Discussion Papers 54, Leibniz Institute of Agricultural Development in Transition Economies (IAMO).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:251:y:2016:i:2:p:600-612. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.