Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Banzhaf–Coleman and Shapley–Shubik Indices in Games with a Coalition Structure: A Special Case Study

Author : Maria Ekes

Published in: Voting Power and Procedures

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In the paper we deal with the comparison of the Shapley–Shubik index and Banzhaf–Coleman index in games with a coalition structure. We analyze two possible approaches in both cases: we calculate voters’ power in a composite game or we apply the modification of original indices proposed by Owen for games with a priori unions. The behavior of both indices is compared basing on the voting game with 100 voters and different coalition structures. We analyze changes of power (measured by means of BC index and SS index) implied by changes of the size and composition of coalition structures as well as by different methodology of measuring the voters’ power (composite game versus game with a priori unions).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Aspects of Power Overlooked by Power Indices
next chapter Pathology or Revelation? The Public Good Index
Literature
Albizuri, M. J. (2000). An axiomatization of the modified Banzhaf-Coleman index. Discussion Papers, Department of Applied Economics IV Basque Country University, No 8.
Banzhaf, J. F. (1965). Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review, 19, 317–343.
Coleman, J. S. (1964). Introduction to mathematical sociology. New York: Free Press of Glencoe.
Dubey, P. (1975). On the uniqueness of the Shapley value. International Journal of Game Theory, 4, 131–139.CrossRef
Ekes, M. (2006). Two types of the Banzhaf–Coleman index in games with a priori unions. Roczniki Kolegium Analiz Ekonomicznych SGH, zeszyt, 15, 31–45.
Felsenthal, D. S., & Machover, M. (1998). The measurement of voting power theory and practice. Problems and paradoxes. Cheltenham: Edward Elgar Publishing.
Hart, S., & Kurz, M. (1983). On the endogenous formation of coalitions. Econometrica, 51, 1295–1313.CrossRef
Laruelle, A., & Valenciano, F. (2004). On the meaning of Owen-Banzhaf coalitional value in voting situations. Theory and Decision, 56, 113–123.CrossRef
Leech, D., & Leech, R. (2006). Voting power and voting blocs. Public Choice, 127, 285–303.CrossRef
Owen, G. (1977). Values of games with a priori unions. In R. Henn & O. Moschlin (Eds.), Lecture notes in economics and mathematical systems. Essays in honour of Oskar Morgenstern (pp. 76–88). New York: Springer.
Owen, G. (1978). Characterization of the Banzhaf-Coleman index. SIAM Journal of Applied Mathematics, 35, 315–327.CrossRef
Owen, G. (1981). Modification of the Banzhaf-Coleman index for games with a priori unions. In M. J. Holler (Ed.), Power, voting and voting power (pp. 232–238). Wurzburg: Physica.CrossRef
Penrose, L. S. (1946). The elementary statistics of majority voting. Journal of the Royal Statistical Society, 109, 53–57.CrossRef
Shapley, L. S. (1953). A value for n-person games, in contributions to the theory of games II. In H. W. Kuhn & A. W. Tucker (Eds.), Annals of mathematics studies (Vol. 28, pp. 307–317). Princeton: Princeton University Press.
Shapley, L. S., & Shubik, M. (1954). A method for evaluating the distributions of power in a committee system. American Political Science Review, 48, 787–792.CrossRef
Metadata
Title
Banzhaf–Coleman and Shapley–Shubik Indices in Games with a Coalition Structure: A Special Case Study
Author
Maria Ekes
Copyright Year
2014
Book
Voting Power and Procedures

Print ISBN: 978-3-319-05157-4

Electronic ISBN: 978-3-319-05158-1

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-05158-1_13