Skip to main content

Voting Power Indices

  • Living reference work entry
  • First Online:
Encyclopedia of Law and Economics
  • 97 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • Alonso-Meijide JM, Bowles C, Holler MJ, Napel S (2009) Monotonicity of power in games with a priori unions. Theory and Decision 66:17–37

    Article  Google Scholar 

  • Banzhaf JF (1965) Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Review 19:317–343

    Google Scholar 

  • Berg S, Holler MJ (1986) Randomized decision rules in voting games: a model of strict proportional power. Quality and Quantity 20:419–429

    Article  Google Scholar 

  • Brams SJ (1975) Game theory and politics. Free Press, New York

    Google Scholar 

  • Deegan J Jr, Packel EW (1979) A new index of power for simple n-person games. International Journal of Game Theory 7:113–123

    Article  Google Scholar 

  • 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 391–404

    Chapter  Google Scholar 

  • Felsenthal DS, Machover M (2005) Voting power measurement: a story of misreinvention. Social Choice and Welfare 25:485–506

    Article  Google Scholar 

  • Freixas J, Kurz S (2016) The cost of getting local monotonicity. Eur J Oper Res 251:600–612

    Google Scholar 

  • 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 57–68

    Google Scholar 

  • 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 193–203

    Google Scholar 

  • 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 169–186

    Chapter  Google Scholar 

  • 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-Wien

    Google Scholar 

  • Holler MJ (1982) Forming coalitions and measuring voting power. Political Studies 30:262–271

    Article  Google Scholar 

  • Holler MJ (1985) Strict proportional power in voting bodies. Theory and Decision 19:249–258

    Article  Google Scholar 

  • Holler MJ, Widgrén M (eds) (2009) Essays in honor of Hannu Nurmi: Volume I (Homo Oeconomicus 26). Accedo, Munich

    Google Scholar 

  • Holler MJ, Nohn A, Vartiainen H (eds) (2011) Essays in honor of Hannu Nurmi: Volume II (Homo Oeconomicus 28). Accedo, Munich

    Google Scholar 

  • Holler MJ, Packel EW (1983) Power, luck and the right index. Zeitschrift für Nationalökonomie (Journal of Economics) 43:21–29

    Article  Google Scholar 

  • Napel S, Widgrén M (2011) Strategic versus non-strategic voting power in the EU Council of Ministers: the consultation procedure. Social Choice and Welfare 37:511–541

    Article  Google Scholar 

  • 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 307–17

    Google Scholar 

  • Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in a committee system. American political Science Review 48:787–792

    Article  Google Scholar 

  • Turnovec F (2011) Strict proportional power and optimal quota. Homo Oeconomicus 27:463–479

    Google Scholar 

  • Weber M (1948[1924]) Class, status and party. In: Gerth HH, C. Wright Mills CW (eds), Essays from Max Weber, Routledge/Kegan Paul, London

    Google Scholar 

Further Reading

  • Felsenthal D, Machover M (1998) The measurement of voting power. Theory and practice, problems and paradoxes. Edward Elgar, Cheltenham

    Google Scholar 

  • Holler MJ, Owen G (eds) (2001) Power indices and coalition formation. Kluwer, Boston/Dordrecht/London

    Google Scholar 

  • Holler MJ, Nurmi H (eds) (2013) Power, voting and voting power: 30 years after. Springer, Heidelberg

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manfred J. Holler .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Holler, M.J. (2016). Voting Power Indices. In: Marciano, A., Ramello, G. (eds) Encyclopedia of Law and Economics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7883-6_503-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-7883-6_503-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7883-6

  • eBook Packages: Springer Reference Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences

Publish with us

Policies and ethics