Encyclopedia of Law and Economics

2019 Edition
| Editors: Alain Marciano, Giovanni Battista Ramello

Voting Power Indices

  • Manfred J. HollerEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7753-2_503

Abstract

This entry introduces Shapley-Shubik index, Banzhaf index, Deegan-Packel index and Public Good Index. It discusses the properties of these measures of a priori voting power focusing on monotonicity. Applications are listed.

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References

  1. Alonso-Meijide JM, Bowles C, Holler MJ, Napel S (2009) Monotonicity of power in games with a priori unions. Theory and Decision 66:17–37CrossRefGoogle Scholar
  2. Banzhaf JF (1965) Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Review 19:317–343Google Scholar
  3. Berg S, Holler MJ (1986) Randomized decision rules in voting games: a model of strict proportional power. Quality and Quantity 20:419–429CrossRefGoogle Scholar
  4. Brams SJ (1975) Game theory and politics. Free Press, New YorkGoogle Scholar
  5. Deegan J Jr, Packel EW (1979) A new index of power for simple n-person games. International Journal of Game Theory 7:113–123CrossRefGoogle Scholar
  6. De Meur G, Gassner M (1987) Problems of equity in multiparty representational systems: What we want and what we can’t. In: Holler MJ (ed) The Logic of multiparty systems. Kluwer, Dordrecht/Boston/Lancaster, pp 391–404CrossRefGoogle Scholar
  7. Felsenthal DS, Machover M (2005) Voting power measurement: a story of misreinvention. Social Choice and Welfare 25:485–506CrossRefGoogle Scholar
  8. Freixas J, Kurz S (2016) The cost of getting local monotonicity. Eur J Oper Res 251:600–612CrossRefGoogle Scholar
  9. Gambarelli G, Owen G (2002) Power in political and business structures. In: Holler MJ, Kliemt H, Schmidtchen D, Streit ME (eds) Power and fairness (Jahrbuch für Neue Politische Ökonomie 20). Mohr Siebeck, Tübingen, pp 57–68Google Scholar
  10. Gambarelli G, Pesce S (2004) Takeover prices and portfolio theory. In: Gambarelli G (ed) Essays on cooperative games: in honor of Guillermo Owen. Special issue of Theory and Decision. Kluwer Academic Publishers, Dordrecht, vol 36. pp 193–203Google Scholar
  11. Gambarelli G, Palestini A (2013) Minimax multi-district apportionments. In: Holler MJ, Nurmi H (eds) Power, voting and voting power: 30 years after. Springer, Heidelberg, pp 169–186CrossRefGoogle Scholar
  12. Grofman B, Scarrow H (1979) Iannucci and its aftermath: the application of the Banzhaf index to weighted voting in the state of New York. In: Brams SJ, Schotter A, Schwödiauer G (eds) Applied game theory. Physica, Würzburg-WienGoogle Scholar
  13. Holler MJ (1982) Forming coalitions and measuring voting power. Political Studies 30:262–271CrossRefGoogle Scholar
  14. Holler MJ (1985) Strict proportional power in voting bodies. Theory and Decision 19:249–258CrossRefGoogle Scholar
  15. Holler MJ, Widgrén M (eds) (2009) Essays in honor of Hannu Nurmi: Volume I (Homo Oeconomicus 26). Accedo, MunichGoogle Scholar
  16. Holler MJ, Nohn A, Vartiainen H (eds) (2011) Essays in honor of Hannu Nurmi: Volume II (Homo Oeconomicus 28). Accedo, MunichGoogle Scholar
  17. Holler MJ, Packel EW (1983) Power, luck and the right index. Zeitschrift für Nationalökonomie (Journal of Economics) 43:21–29CrossRefGoogle Scholar
  18. Napel S, Widgrén M (2011) Strategic versus non-strategic voting power in the EU Council of Ministers: the consultation procedure. Social Choice and Welfare 37:511–541CrossRefGoogle Scholar
  19. Shapley LS (1953) A value for n-person cooperative games. In: Kuhn H, Tucker AW (eds) Contributions to the theory of games, vol 28, Annals of mathematical studies. Princeton University Press, Princeton, pp 307–17Google Scholar
  20. Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in a committee system. American political Science Review 48:787–792CrossRefGoogle Scholar
  21. Turnovec F (2011) Strict proportional power and optimal quota. Homo Oeconomicus 27:463–479Google Scholar
  22. Weber M (1948[1924]) Class, status and party. In: Gerth HH, C. Wright Mills CW (eds), Essays from Max Weber, Routledge/Kegan Paul, LondonGoogle Scholar

Further Reading

  1. Felsenthal D, Machover M (1998) The measurement of voting power. Theory and practice, problems and paradoxes. Edward Elgar, CheltenhamGoogle Scholar
  2. Holler MJ, Owen G (eds) (2001) Power indices and coalition formation. Kluwer, Boston/Dordrecht/LondonGoogle Scholar
  3. Holler MJ, Nurmi H (eds) (2013) Power, voting and voting power: 30 years after. Springer, HeidelbergGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center of Conflict Resolution (CCR)University of Hamburg, Institute of SocioEconomics (ISE)HamburgGermany