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Effectivity and Power

Author

Listed:
  • Karos, Dominik

    (Microeconomics & Public Economics, RS: GSBE ETBC)

  • Peters, Hans

    (QE Math. Economics & Game Theory, RS: GSBE ETBC)

Abstract

We axiomatically develop a class of power indices for effectivity functions, both for the case where the set of alternatives is finite and where it is infinite. Such power indices make it possible to take the issues under consideration into account, in contrast to power indices defined just for simple games. As an example, we consider the US legislative system. We also show that our approach can be used to develop power indices for spatial political games.

Suggested Citation

  • Karos, Dominik & Peters, Hans, 2016. "Effectivity and Power," Research Memorandum 034, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2016034
    DOI: 10.26481/umagsb.2016034
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    References listed on IDEAS

    as
    1. Grofman, Bernard & Owen, Guillermo & Noviello, Nicholas & Glazer, Amihai, 1987. "Stability and Centrality of Legislative Choice in the Spatial Context," American Political Science Review, Cambridge University Press, vol. 81(2), pages 539-553, June.
    2. Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
    3. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    4. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
    5. Enelow,James M. & Hinich,Melvin J., 1984. "The Spatial Theory of Voting," Cambridge Books, Cambridge University Press, number 9780521275156.
    6. Dan Felsenthal & Moshé Machover, 2005. "Voting power measurement: a story of misreinvention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 485-506, December.
    7. Cesarino Bertini & Josep Freixas & Gianfranco Gambarelli & Izabella Stach, 2013. "Comparing Power Indices," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-19.
    8. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    9. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    10. repec:dau:papers:123456789/13220 is not listed on IDEAS
    11. Yves Crama & Luc Leruth, 2013. "Power Indices And The Measurement Of Control In Corporate Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-15.
    12. Crama, Yves & Leruth, Luc, 2007. "Control and voting power in corporate networks: Concepts and computational aspects," European Journal of Operational Research, Elsevier, vol. 178(3), pages 879-893, May.
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    Cited by:

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    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. Christian Basteck & Ulysse Lojkine, 2025. "Power and Freedom in Mechanisms," Papers 2512.10112, arXiv.org, revised May 2026.
    4. Michele Aleandri & Felix Fritz & Stefano Moretti, 2025. "Desirability and social ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 65(3), pages 721-763, November.
    5. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.
    6. Albizuri, M.J. & Goikoetxea, A., 2022. "Probabilistic Owen-Shapley spatial power indices," Games and Economic Behavior, Elsevier, vol. 136(C), pages 524-541.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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