Skip to main content

Coalition Configurations and the Public Good Index

  • Chapter
  • First Online:
Power, Voting, and Voting Power: 30 Years After

Abstract

In games with a coalition structure, players organize themselves in coalitions that form a partition of the set of players. In games with a coalition configuration, the union of the coalitions is the whole set of players but the coalitions are not necessarily disjoint. We introduce two variations of the Public Good Index for games with a coalition configuration, provide axiomatic characterizations of them, and apply them to a real world example.

This chapter has been published in Homo Oeconomicus 29 (3), 2012.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Albizuri, M. J., & Aurrekoetxea, J. (2006). Coalition configurations and the Banzhaf index. Social Choice and Welfare, 26, 571–596.

    Article  Google Scholar 

  • Albizuri, M. J., Aurrekoetxea, J., & Zarzuelo, J. M. (2006). Configuration values: Extensions of the coalitional Owened value. Games and Economic Behaviour, 57, 1–17.

    Google Scholar 

  • Alonso-Meijide, J. M., Casas-Méndez, B., Fiestras-Janeiro, M. G., & Holler, M. J. (2010a). Two variations of the public good index for games with a priori unions. Control and Cybernetics, 39, 839–855.

    Google Scholar 

  • Alonso-Meijide, J. M., Casas-Méndez, B., Fiestras-Janeiro, M. G., Holler, M. J., & Nohn, A. (2010b). Axiomatizations of public good indices with a priori unions. Social Choice and Welfare, 35, 517–533.

    Article  Google Scholar 

  • Andjiga, N., & Courtin, S. (2010). Coalition configuration and share functions. Working paper: CREM, Université de Caen, France.

    Google Scholar 

  • Banzhaf, J. F. (1965). Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review, 19, 317–343.

    Google Scholar 

  • Coleman, J. S. (1971), Control of collectivities and the power of a collectivity to act. In: B. Lieberman (Ed.), Social choice (pp. 269–300). New York: Gordon and Breach.

    Google Scholar 

  • Deegan, J., & Packel, E. W. (1978). A new index of power for simple n-person games. International Journal of Game Theory, 7, 113–123.

    Google Scholar 

  • Holler, M. J. (1982). Forming coalitions and measuring voting power. Political Studies, 30, 262–271.

    Article  Google Scholar 

  • Holler, M. J., & Nohn, A. (2009). The public good index with threats in a priori unions. Essays in Honor of Hannu Nurmi, Vol. I, Homo Oeconomicus, 26, 393–401.

    Google Scholar 

  • Holler, M. J., & Packel, E. W. (1983). Power, luck and the right index. Journal of Economics, 43, 21–29.

    Article  Google Scholar 

  • Johnston, R. J. (1978). On the measurement of power: Some reaction to Laver. Environment and Planning A, 10, 907–914.

    Article  Google Scholar 

  • Owen, G. (1977). Values of games with a priori unions. In R. Henn & O. Moeschlin (Eds.), Mathematical economics and game theory (pp. 76–88). Heidelberg: Springer Verlag.

    Google Scholar 

  • Shapley, L. S. (1953). A value for n-person games. Annals of Mathematics Studies, 28, 307–318.

    Google Scholar 

  • Shapley, L. S., & 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 

  • van der Laan, G., & van den Brink, R. (2002). A Banzhaf share function for cooperative games with coalition structure. Theory and Decision, 53, 61–86.

    Article  Google Scholar 

  • van der Laan, G., & van den Brink, R. (2005). A class of consistent share function for games with coalition structure. Games and Economic Behavior, 51, 193–212.

    Article  Google Scholar 

  • Winter, E. (1992). The consistency and potential for values with coalition structures. Games and Economic Behavior, 4, 132–144.

    Article  Google Scholar 

Download references

Acknowledgments

This research received financial support from the Academy of Finland, as well as from Ministerio de Ciencia e Innovación (Spain) and FEDER through Projects ECO2008-03484-C02-02, MTM2011-27731-C03-02 and MTM2011-27731-C03-03 and from Xunta de Galicia through Project INCITE09-207-064-PR.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to José M. Alonso-Meijide .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Alonso-Meijide, J.M., Casas-Méndez, B., Fiestras-Janeiro, M.G., Holler, M.J., Nohn, A. (2013). Coalition Configurations and the Public Good Index. In: Holler, M., Nurmi, H. (eds) Power, Voting, and Voting Power: 30 Years After. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35929-3_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35929-3_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35928-6

  • Online ISBN: 978-3-642-35929-3

  • eBook Packages: Business and EconomicsEconomics and Finance (R0)

Publish with us

Policies and ethics