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Power Indices Methodology: Decisiveness, Pivots, and Swings

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Abstract

Three most frequently used measures of a priori voting power of members of a committee were proposed by Shapley and Shubik (1954), Penrose (1946) and Banzhaf (1965), and Holler and Packel (1983). We shall refer to them also as SS-power index, PB-power index and HP-power index. There exist also some other well defined power indices, such as Johnston index (1978) and Deegan-Packel index (1979).1

For a comprehensive survey and analysis of power indices methodology, see Felsenthal and Machover (1998).

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References

  • Banzhaf, J.F. (1965) Weighted Voting Doesn’t Work: A Mathematical Analysis. Rutgers Law Review 19: 317–343.

    Google Scholar 

  • Deegan, J. and Packel, E.W. (1979) A New Index of Power for Simple n-person Games. International Journal of Game Theory 7: 113–123.

    Article  Google Scholar 

  • Felsenthal, D.S. and Machover, M. (1998) The Measurement of Voting Power, Edward Elgar.

    Google Scholar 

  • Felsenthal, D.S. and Machover, M. (2004), A Priori Voting Power: What is it About? Political Studies Review 2: 1–23.

    Article  Google Scholar 

  • Felsenthal, D.S., Machover, M., and Zwicker, W. (1998) The Bicameral Postulates and Indices of A Priori Voting Power, Theory and Decisions 44: 83–116.

    Article  Google Scholar 

  • Hall, M. (1967) Combinatorial Theory. Blaisdell Publishing Company.

    Google Scholar 

  • Holler, M.J. and Packel, E.W. (1983) Power, Luck and the Right Index, Zeitschrift fűr Nationalökonomie (Journal of Economics) 43: 21–29.

    Article  Google Scholar 

  • Holler, M.J. and Li, X. (1995) From Public Good Index to Public Value. An Axiomatic Approach and Generalization, Control and Cybernetics 24: 257–270.

    Google Scholar 

  • Johnston, R.J. (1978) On the Measurement of Power: Some Reactions to Laver, Environment and Planning 10: 907–914.

    Article  Google Scholar 

  • Nurmi, H. (1997), On Power Indices and Minimal Winning Coalitions, Control and Cybernetics 26: 609–611.

    Google Scholar 

  • Owen, G. (1982) Game Theory (2nd ed.), Academic Press.

    Google Scholar 

  • Penrose, L.S. (1946) The Elementary Statistics of Majority Voting, Journal of the Royal Statistical Society 109: 53–57.

    Article  Google Scholar 

  • Shapley, L.S. (1953) A Value for n-Person Games, in H.W. Kuhn and A.W. Tucker (eds), Contributions to the Theory of Games II, Princeton University Press, 307–317.

    Google Scholar 

  • Shapley, L.S. and 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. (2004) Power Indices: Swings or Pivots? in Matti Wiberg (ed.) Reasoned Choice, Finnish Political Science Association.

    Google Scholar 

  • Turnovec, F., Mercik, J.W., and Mazurkiewicz, M. (2004), Power Indices: Shapley-Shubik or Penrose-Banzhaf? in R. Kulikowski, J. Kacprzyk, and R. Slowinski (eds) Badania Operacyjne i Systemowe 2004, Podejmowanie Decyzji, Podstawy Metodyczne i Zastosowania, EXIT, Warszawa.

    Google Scholar 

  • Turnovec, F. (2007) New Measure of Voting Power, Czech Economic Review (Acta Universitatis Carolinae Oeconomica) 1: 1–11.

    Google Scholar 

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Turnovec, F., Mercik, J.W., Mazurkiewicz, M. (2008). Power Indices Methodology: Decisiveness, Pivots, and Swings. In: Braham, M., Steffen, F. (eds) Power, Freedom, and Voting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73382-9_2

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