Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Common behaviour of power indices

Abstract

The variations ensuing in a weighted majority game are studied when a player increases his weight in prejudice of others or decreases in favor, or trades shares outside the game (in particular when an-person game becomes an (n+1)-person one). An invariant behaviour for different game values is found for all these cases. Possible applications to politics, shareholdings and large games are pointed out.

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

References

  1. Arcaini, G., andG. Gambarelli: Algorithm of Shapley Value Variation in Shares Trading. Forthcoming, 1982.

  2. Aumann, R.J., andL.S. Shapley: Values of Non-Atomic Games. Princeton 1974.

  3. Banzhaf, J.F.: Weighted Voting Doesn't Work: a Mathematical Analysis. Rutgers Law Review19, 1965, 317–343.

  4. Brams, S.J.: Paradoxes in Politics. New York 1976.

  5. Dubey, P.: Some results on values of finite and infinite games. Tech. Report, Center of Applied Mathematics, Cornell University, Ithaca, NY 14853, 1975.

  6. Gambarelli, G.: The “Control Quota” Component in the Price of Shares. Int. Days of Finance, AFFI, Strasbourg, Univ. L. Pasteur, June 12–14, 1980. Or Riv. di Mat. per le Sc. Econ. e Soc.IV (1), 1982a, 29–39.

  7. —: Portfolio Selection and Firms' Control. VIII Ann. Math. of the European Finance Association, Sheveningen, the Netherlands, Sept. 11–12, 1981, Or Finance3 (I), 1982b, 69–83.

  8. Lucas, W.F.: Measuring Power in Weighted Voting Systems. Case Studies in Applied Mathematics, MAA Special Projects Office, Dept. of Math., California State Univ. at Hayward 94542. Or Tech. Rep. 227, Dept. of Op. Res., Cornell Univ., Ithaca, NY 14853, 1976.

  9. Mann, I., andL.S. Shapley: Value of Large Games, VI: Evaluating the Electoral College Exactly. Rand Corp., RM 3158, S. Monica, CA, 1962.

  10. Milnor, J.W., andL.S. Shapley: Values of Large Games II: Oceanic Games. Rand Corp., RM 2649, S. Monica, CA, 1961.

  11. Papayanopoulos, L.: Democratic Representation and Apportionment: Quantitative Methods, Measures and Criteria. Annals of N.Y. Academy of Sciences, Vol. 219, 1973.

  12. Pressacco, F.: Arbitraggi bilanciati per giochi omogenei di maggioranza ponderata. Rivista di Matematica per le Sc. Econ. e Soc.I (1), 1978.

  13. Shapiro, N.Z., andL.S. Shapley: Values of Large Games, I: A limit theorem. Rand Corp., RM 2648, S. Monica, CA, 1960.

  14. Shapley, L.S., andM. Shubik: A method for evaluating the distribution of power in a committee system. American Political Science Review48, 1954, 787–792.

Download references

Author information

Additional information

Sponsored by the GNAFA of the Consiglio Nazionale delle Ricerche.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gambarelli, G. Common behaviour of power indices. Int J Game Theory 12, 237–244 (1983). https://doi.org/10.1007/BF01769093

Download citation

Keywords

  • Economic Theory
  • Game Theory
  • Power Index
  • Weighted Majority
  • Common Behaviour