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A Public Help Index

In: Power, Freedom, and Voting

Author

Listed:
  • Cesarino Bertini

    (University of Bergamo)

  • Gianfranco Gambarelli

    (University of Bergamo)

  • Izabella Stach

    (AGH University of Science and Technology)

Abstract

As far as we known, the first concept of power index dates back to 1780s and is due to Luther Martin (see Felsenthal and Machover (2005), Gambarelli and Owen (2004) and Riker (1986)). Lionel S. Penrose (1946) gave, probably, the first scientific discussion of voting power where he introduced the concept of a priori voting power (a similar analysis was independently carried out by John F. Banzhaf (1965)). Lloyd S. Shapley, in cooperation with Martin Shubik (Shapley and Shubik 1954), came up with a specialization of the Shapley (1953) value as a power index. Other power indices were introduced later; some derived from existing values, others built exclusively for simple games. The Public Good Index introduced by Manfred Holler in (1978) belongs to the latter category.

Suggested Citation

  • Cesarino Bertini & Gianfranco Gambarelli & Izabella Stach, 2008. "A Public Help Index," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 5, pages 83-98, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-73382-9_5
    DOI: 10.1007/978-3-540-73382-9_5
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    Citations

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    Cited by:

    1. Izabella Stach, 2022. "Reformulation of Public Help Index θ Using Null Player Free Winning Coalitions," Group Decision and Negotiation, Springer, vol. 31(2), pages 317-334, April.
    2. Gianfranco Gambarelli & Angelo Uristani, 2009. "Multicameral voting cohesion games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(4), pages 433-460, December.
    3. 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.
    4. Somdeb Lahiri, 2021. "Pattanaik's axioms and the existence of winners preferred with probability at least half," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 109-122.

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