Why Power Indices and Coalition Formation?

  • Manfred J. Holler
  • Guillermo Owen


This introductory note discusses the main arguments that motivate the growing interest in power indices and the theory of coalition formation that also determine the selection of contributions to this volume. The main arguments are those of substantial growth in the application of power indices to political institutions, especially the European Union, the intensive discussion of the monotonicity properties of various indices, and the probabilistic interpretation of power, coalition formation, and power measures.


Power Index European Central Bank Median Voter Coalition Formation Winning Coalition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allingham, M.G. (1975), “Economic Power and Values of Games”, Zeitschrift für Nationalökonomie (Journal of Economics), 35, 293–299.CrossRefGoogle Scholar
  2. Barry, B. (1980), “Is it Better to be Powerful or Lucky: Part I and Part II”, Political Studies, 28, 183–194 and 338–352.Google Scholar
  3. Brams, S.J., and P.C. Fishburn (1995), “When is Size a Liability? Bargaining Power in Minimal Winning Coalitions”, Journal of Theoretical Politics, 7, 301–316.CrossRefGoogle Scholar
  4. Coleman, J.S. (1971), “Control of Collectivities and the Power of a Collectivity to Act”, in: B. Lieberman (ed.), Social Choice, New York: Gordon and Breach.Google Scholar
  5. Downs, A. (1957), An Economic Theory of Democracy, New York: Harper and Row.Google Scholar
  6. Dreyer, J., and A. Schotter (1980), “Power Relationship in the International Monetary Fund: The Consequences of Quota Changes”, Review of Economics and Statistics, 62, 97–106.CrossRefGoogle Scholar
  7. Dubey, P., and L.S. Shapley (1979), “Mathematical Properties of the Banzhaf Power Index”, Mathematics of Operations Research, 4, 99–131.CrossRefGoogle Scholar
  8. Felsenthal, D., and M. Machover (1995), “Postulates and Paradoxes of Relative Voting Power–A Critical Appraisal”, Theory and Decision, 38, 195–229.CrossRefGoogle Scholar
  9. Felsenthal, D., and M. Machover (1998), The Measurement of Voting Power. Theory and Practice, Problems and Paradoxes, Cheltenham: Edward Elgar.Google Scholar
  10. Felsenthal, D., M. Machover, and W. Zwicker (1998), “The Bicameral Postulates and Indices of A Priori Voting Power”, Theory and Decision, 44, 83–116.CrossRefGoogle Scholar
  11. Fishbum, P.C., and S.J. Brams (1996), “Minimal Winning Coalitions in Weighted-Majority Voting Games”, Social Choice and Welfare, 13, 397–417.CrossRefGoogle Scholar
  12. Fishburn, P.C., and W.V. Gehrlein (1977), “Collective Rationality versus Distribution of Power of Binary Social Choice Functions”, Journal of Economic Theory, 16, 72–91.CrossRefGoogle Scholar
  13. Freixas, J., and G. Gambarelli (1997), “Common Internal Properties Among Power Indices”, Control and Cybernetics, 26, 591–603.Google Scholar
  14. Garrett, G., and G. Tsebelis (1999), “Why Resist the Temptation to Apply Power Indices to the EU”, Journal of Theoretical Politics, 11, 321–331.CrossRefGoogle Scholar
  15. Holler, M.J. (1978), “A Priori Party Power and Government Formation”, Munich Social Science Review, 1, 25–41 (reprinted in: M.J. Holler (ed.) (1982), Power, Voting, and Voting Power, Würzburg-Vienna: Physica.).Google Scholar
  16. Holler, M.J. (1982), “Forming Coalitions and Measuring Voting Power”, Political Studies, 30, 262–271.CrossRefGoogle Scholar
  17. Holler, M.J. (1997), “Power Monotonicity and Expectations”, Control and Cybernetics, 26, 605–607.Google Scholar
  18. Holler, M.J., and E.W. Packel (1983), “Power, Luck and the Right Index”, Zeitschrift fiir Nationalökonomie (Journal of Economics), 43, 21–29.CrossRefGoogle Scholar
  19. Holler, M.J., R. Ono, and F. Steffen (1999), “Constrained Monotonicity and the Measurement of Power”, Beiträge zur Wirtschaftsforschung, No. 107, Sozial-ökonomisches Seminar der Universität Hamburg.Google Scholar
  20. Holler, M.J., and M. Widgrén (1999), “Why Power Indices for Assessing EU Decision-Making?”, Journal of Theoretical Politics, 11, 291–308.CrossRefGoogle Scholar
  21. Isbell, J.R. (1958), “A Class of Simple Games”, Duke Mathematics Journal, 25, 423–439.CrossRefGoogle Scholar
  22. Machover, M. (2000), “Notions of A Priori Voting Power: Critique of Holler and Widgrén”, Homo Oeconomicus, 16, 415–426.Google Scholar
  23. Miller, N.R. (1982), “Power in Game Forms”, in: M.J. Holler (ed.), Power, Voting, and Voting Power, Würzburg-Vienna: Physica (reprinted in Homo Oeconomicus, 16, 1999, 219–243 ).Google Scholar
  24. Napel, S., and M. Widgrén (2001), “The Power of an Inferior Player”, Jahrbuch für Neue Politische Ökonomie, 20, Tübingen: Mohr-Siebeck.Google Scholar
  25. Nurmi, H. (1998), Rational Behaviour and the Design of Institutions: Concepts, Theories and Models, Cheltenham, UK, and Northampton, MA: Edward Elgar.Google Scholar
  26. Owen, G. (1972), “Multilinear Extensions of Games”, Management Science, 18, 64–79.CrossRefGoogle Scholar
  27. Owen, G. (1975), “Multilinear Extensions and the Banzhaf Value”, Naval Research Logistics Quarterly, 22, 741–750.CrossRefGoogle Scholar
  28. Owen, G. (1977), “Values of Games with A Priori Unions”, in: R. Henn, and O. Moeschlin (eds.), Essays in Mathematical Economics and Game Theory, Berlin and New York: Springer-Verlag, 76–88.CrossRefGoogle Scholar
  29. Owen G. (1982), “Modification of the Banzhaf-Coleman Index for Games with A Priori Unions”, in: M.J. Holler (ed.), Power, Voting, and Voting Power, Würzburg-Vienna: Physica.Google Scholar
  30. Schotter, A. (1982), “The Paradox of Redistribution: Some Theoretical and Empirical Results”, in: M.J. Holler (ed.), Power, Voting, and Voting Power, Würzburg-Vienna: Physica.Google Scholar
  31. Shapley, L.S. (1953), “A Value for n-Person Games”, in: H. Kuhn, and A.W. Tucker (eds.), Contributions to the Theory of Games II, Princeton: Princeton University Press.Google Scholar
  32. Shapley, L.S., and M. Shubik (1954), “A Method of Evaluating the Distribution of Power in a Committee System”, American Political Science Review, 48, 787–792.CrossRefGoogle Scholar
  33. Stenlund, H., J.-E. Lane, and B. Bjurulf (1985), “Formal and real voting power”, European Journal of Political Economy, 1, 59–75.CrossRefGoogle Scholar
  34. Straffin, P.D. (1977), Homogeneity, Independence, and Power Indices“, Public Choice, 30, 107–118.CrossRefGoogle Scholar
  35. Straffin, P.D. (1988), “The Shapley-Shubik and the Banzhaf Power Index as Probabilities”, in: A.E. Roth (ed.), The Shapley Value: Essays in Honor of Lloyd S. Shapley, Cambridge: Cambridge University Press.Google Scholar
  36. Tsebelis, G., and G. Garrett (1996), “Agenda Setting Power, Power Indices, and Decision-Making in the European Union”, International Review of Law and Economics, 16, 345–361.CrossRefGoogle Scholar
  37. Tsebelis, G., and G. Garrett (1997), “Why Power Indices Cannot Explain Decisionmaking in the European Union”, in: D. Schmidtchen, and R. Cooter (eds.) Constitutional Law and Economics of the European Union, Cheltenham, UK: Edward Elgar.Google Scholar
  38. Turnovec, F. (1997), “Power, Power Indices and Intuition”, Control and Cybernetics, 26, 613–615.Google Scholar
  39. Turnovec, F. (1998), “Monotonicity and Power Indices”, in: T.J. Stewart, and R.C. van den Honert (eds.), Trends in Multicriteria Decision-Making, Lecture Notes in Economics and Mathematical Systems 465, Berlin et al.: Springer-Verlag.Google Scholar
  40. Widgren, M. (1994), “Voting Power in the EC and the Consequences of Two Different Enlargements”, European Economic Review, 38, 1153–1170.CrossRefGoogle Scholar
  41. Widgren, M. (1995), “Probabilistic Voting Power in the EU Council: the Cases of Trade Policy and Social Regulation”, Scandinavian Journal of Economics, 97, 345–356.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Manfred J. Holler
    • 1
  • Guillermo Owen
    • 2
  1. 1.Institute of SocioEconomicsUniversity of HamburgHamburgGermany
  2. 2.Department of MathematicsNaval Postgraduate SchoolMontereyUSA

Personalised recommendations