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Power Indices in Politics

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Political and Related Models

Part of the book series: Modules in Applied Mathematics ((MAM))

Abstract

“Political science, as an empirical discipline, is the study of the shaping and sharing of power” (Lasswell and Kaplan in Power and Society, 1950).

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References

  1. Allingham, M. G. “Economic Power and the Values of Games,” Zeitschrift für Nationalökonomie, 35 (1975), 293–299.

    Article  Google Scholar 

  2. Aumann, R. J., and Shapley, L. S. Values of Non-Atomic Games, Princeton University Press, Princeton, New Jersey, 1974.

    Google Scholar 

  3. Bain, Richard, and Parris, Judith. Convention Decisions and Voting Records, Brookings Institution, Washington, D.C., 1973.

    Google Scholar 

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

    Google Scholar 

  5. Brams, S. J. Game Theory and Politics, Free Press, 1975.

    Google Scholar 

  6. Brams, S. J. Paradoxes in Politics, Free Press, 1976.

    Google Scholar 

  7. Brams, S. J., and Riker, W. H. “Models of Coalition Formation in Voting Bodies,” Mathematical Applications in Political Science VI (Herndon and Bernd eds.), pp. 79–124. University of Virginia Press, Charlottesville, 1972.

    Google Scholar 

  8. Canada, Constitutional Conference Proceedings, Victoria, B. C. June 14, 1971, Information Canada, Ottawa.

    Google Scholar 

  9. Caplow, Theodore, Two Against One: Coalitions in Triads, Prentice-Hall, Englewood Cliffs, New Jersey, 1968.

    Google Scholar 

  10. Coleman, James “Control of Collectivities and the Power of a Collectivity to Act,” Social Choice, (Lieberman, ed.), pp. 277–287. Gordon and Breach, 1971.

    Google Scholar 

  11. Deegan, J., and Packel, E. “To the (Minimal) Victors Go the (Equally Divided) Spoils: a New Power Index,” 1982. Chapter 10 in this volume.

    Google Scholar 

  12. Dubey, Pradeep. “Some Results on Values of Finite and Infinite Games,” Technical Report, Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, 1975.

    Google Scholar 

  13. Dubey, Pradeep. “On the Uniqueness of the Shapley Value,” International journal of Game Theory, 4 (1975), 131–140.

    Article  Google Scholar 

  14. Dubey, P., and Shapley, L. S. “Mathematical Properties of the Banzhaf Power Index,” Mathematics of Operations Research, 4 (1979), 99–131.

    Article  Google Scholar 

  15. Ellsberg, Daniel. “The Theory and Practice of Blackmail,” Rand Corporation, Santa Monica, 1959.

    Google Scholar 

  16. Kilgour, D. M. “A Shapley Value for Cooperative Games with Quarreling,” Game Theory as a Theory of Conflict Resolution (Rapoport ed.), pp. 193–206. D. Reidel, Boston, 1974.

    Chapter  Google Scholar 

  17. Kleiner, Alex. “A Weighted Voting Model,” Mathematics Magazine, 53 (1980), 28–32.

    Article  Google Scholar 

  18. Lucas, W. F. “Measuring Power in Weighted Voting Systems,” 1982. Chapter 9 in this volume.

    Google Scholar 

  19. Luce, R. D., and Raiffa, H. Games and Decisions, Wiley, New York, 1957.

    Google Scholar 

  20. Martin, Ralph G. Ballots and Bandwagons, Rand McNally, New York, 1964.

    Google Scholar 

  21. Miller, D. R. “A Shapley Value Analysis of the Proposed Canadian Constitutional Amendment Scheme,” Canadian Journal of Political Science, 6 (1973), 140–143.

    Article  Google Scholar 

  22. Milnor, J. W., and Shapley, L. S. “Values of Large Games II: Oceanic Games” RM2649, Rand Corporation, 1961. Reprinted in Mathematics of Operations Research, 3 (1978), 290–307.

    Google Scholar 

  23. Nagel, Jack. The Descriptive Analysis of Power, Yale University Press, New Haven, Connecticut, 1975.

    Google Scholar 

  24. Owen, Guillermo. “Political Games,” Naval Research Logistics Quarterly, 18 (1971), 345–355.

    Article  Google Scholar 

  25. Owen Guillermo. “Multilinear Extensions of Games,” Management Science, Series A, 18 (1972), P64–P79.

    Google Scholar 

  26. Polsby, Nelson. “Decision-making at the National Conventions,” Western Political Quarterly, 13 (1960), 609–619.

    Article  Google Scholar 

  27. Rae, Douglas. “Decision Rules and Individual Values in Constitutional Choice,” American Political Science Review, 63 (1969), 40–56.

    Article  Google Scholar 

  28. Riker, W. H., and Ordeshook, P. An Introduction to Positive Political Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1973.

    Google Scholar 

  29. Roth, Alvin. “Utility Functions for Simple Games,” Journal of Economic Theory, 16 (1977).

    Google Scholar 

  30. Schelling, Thomas. The Strategy of Conflict, Harvard University Press, Cambridge, Massachusetts, 1960.

    Google Scholar 

  31. Shapley, L. S. “Values of Large Games III: A Corporation with Two Large Stockholders,” RM-2650-PR, Rand Corporation, 1961. Reprinted as part of Milnor and Shapley in Mathematics of Operations Research, 3 (1978), 290–307.

    Google Scholar 

  32. Shapley, L. S. “Simple Games: An Outline of the Descriptive Theory,” Behavioral Science, 7 (1962), 59–66.

    Article  Google Scholar 

  33. Shapley, L. S. “Compound Simple Games III: On Committees,” RM-5438-PR, Rand Corporation, 1967.

    Google Scholar 

  34. Shapley, L. S., and Shapiro, N. Z. “Values of Large Games I: A Limit Theorem” RM-2648, Rand Corporation, 1960. Reprinted in Mathematics of Operations Research, 3 (1978), 1–9.

    Article  Google Scholar 

  35. Shapley, L. S., and Shubik, M. “A Method for Evaluating the Distribution of Power in a Committee System,” American Political Science Review, 48 (1954), 787–792.

    Article  Google Scholar 

  36. Straffin, P. D. “The Power of Voting Blocs: An Example,” Mathematics Magazine, 50 (1977), 22–24.

    Article  Google Scholar 

  37. Straffin, P. D. “Homogeneity, Independence, and Power Indices,” Public Choice, 50 (1977), 107–118.

    Article  Google Scholar 

  38. Straffin, P. D. “The Bandwagon Curve,” American Journal of Political Science 21 (1977), 695–709.

    Article  Google Scholar 

  39. Straffin, P. D. “Probability Models for Power Indices,” Game Theory and Political Science (P. C. Ordeshook, ed.), pp. 477–510. New York University Press, 1978.

    Google Scholar 

  40. Straffin, P. D. “Using Integrals to Evaluate Voting Power,” The Two-Year College Mathematics Journal, 10 (1919), 179–181.

    Article  Google Scholar 

  41. Straffm, P. D. Topics in the Theory of Voting, Birkhauser, Boston, 1980. Chapter one.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Beloit College, Beloit, Wisconsin, 53511, USA

    Philip D. Straffin Jr.

Authors
  1. Philip D. Straffin Jr.
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Editor information

Editors and Affiliations

  1. Department of Politics, New York University, New York, NY, 1003, USA

    Steven J. Brams

  2. School of Operations Research, Cornell University, Ithaca, NY, 14853, USA

    William F. Lucas

  3. Department of Mathematics, Beloit College, Beloit, WI, 53511, USA

    Philip D. Straffin Jr.

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© 1983 Springer-Verlag New York Inc.

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Straffin, P.D. (1983). Power Indices in Politics. In: Brams, S.J., Lucas, W.F., Straffin, P.D. (eds) Political and Related Models. Modules in Applied Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5430-0_11

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  • DOI: https://doi.org/10.1007/978-1-4612-5430-0_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-5432-4

  • Online ISBN: 978-1-4612-5430-0

  • eBook Packages: Springer Book Archive

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