Skip to main content
Article thumbnail
Location of Repository

Computing power indices for large voting games

By Dennis Leech


Voting Power Indices enable the analysis of the distribution of power in a legislature or voting body in which different members have different numbers of votes. Although this approach to the measurement of power, based on co-operative game theory, has been known for a long time its empirical application has been to some extent limited, in part by the difficulty of computing the indices when there are many players. This paper presents new algorithms for computing the classical power indices, those of\ud Shapley and Shubik (1954) and of Banzhaf (1963), which are essentially modifications of approximation methods due to Owen, and have been shown to work well in real applications. They are of most utility in situations where both the number of players is large and their voting weights are very non-uniform, some members having considerably larger numbers of votes than others, where Owen's approximation methods are least accurate. The suggestion is made that the availability of such improved algorithms might stimulate further applied research in this field

Topics: HB, QA
Publisher: University of Warwick, Department of Economics
Year: 2002
OAI identifier:

Suggested articles


  1. (1983). [Also Center for the Study of Globalization and Regionalisation Working Papers, 68/01, University of Warwick.] Lucas, William F.
  2. (1954). A Method for Evaluating the Distribution of Power in a doi
  3. (2002). An Empirical Comparison of the Performance of Classical Power Indices," Political Studies, doi
  4. (1983). and H.S.Wilf doi
  5. (1999). Corporate Ownership around the World," doi
  6. (1992). Empirical Analysis of the Distribution of a priori Voting Power: Some Results for the British Labour Party Conference and Electoral College", doi
  7. Evaluation of a Presidential Election Game”, doi
  8. (1995). Game Theory,(3rd Edition)
  9. (1979). Mathematical Properties of the Banzhaf Value," doi
  10. (1998). Measurement of Voting Power, doi
  11. Multilinear Extensions and the Banzhaf Value," doi
  12. (1995). Postulates and Paradoxes of Relative Voting Power: a Critical Re-Appraisal," Theory and Decision, doi
  13. (1994). Power and Stability in Politics," chapter 32 of Aumann, Robert doi
  14. (1981). Power, Voting and Voting Power, doi
  15. (2001). Shareholder Voting Power and Corporate Governance: a Study of Large British Companies,"
  16. (1998). The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision,
  17. (1968). The Optimum Addition of Points to Quadrature Formulae,” doi
  18. (1988). The Relationship between Shareholding Concentration and Shareholder Voting Power in British Companies: a Study of the Application of Power Indices for Simple Games," doi
  19. (2001). The Treaty of Nice and doi
  20. (1962). Values of Large Games VI: Evaluating the Electoral College Exactly, RM-3158, The Rand Corporation ,
  21. (1988). Voting Games, Power Indices and Presidential Elections,"
  22. (1994). Voting Power in the EC Decision Making and the Consequences of Two Different Enlargements," doi
  23. (1965). Weighted Voting Doesn’t Work: A Mathematical Analysis”,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.