Weighted Voting Bibliography (7/11/2001)

Prepared by:

Joseph Malkevitch
Mathematics and Computing Department
York College (CUNY)
Jamaica, New York 11451-0001

Email: malkevitch@york.cuny.edu (for additions, suggestions, and corrections)

Banzhaf, J., Weighted voting does not work: a mathematical analysis, Rutgers Law Review, 19 (1965) 317-343.

Banzhaf, J., One man, 3.312 votes: A mathematical analysis of the electoral college, Villanova Law Review, 13 (1968) 304-332.

Dubey, P., On the uniqueness of the Shapley value, International J. of Game Theory, 4 (1975) 131-139.

Dubey, P., and L. Shapley, Mathematical properties of the Banzhaf power index, Mathematics of Operations Research 4 (1979) 99-131.

Hilliard, M., Weighted voting theory and applications, Tech. Report No. 609, School of Operations Research and Industrial Engineering, Cornell University, 1983.

Imrie, R., The impact of weighted vote on representation in municipal governing bodies of New York state, in L. Papayanopoulos, (ed.), Democratic Represenation and Apportionment: Quantitative Methods, Meaures, and Criteria, Annals of the New York Academy of Sciences, volume 219, 1973, p. 192-199.

Kilgour, D., A formal analysis of the amending formula of Canada's Consitution Act,, Canadial J. of Political Science, 16 (1983) 771-777.

Krohn, I. and P. Sudhšlter, Directed and weighted majority games, Mathematical Methods of Operations Research 42 (1995) 189-216.

Lapidot, E., The counting vector of a simple game, Proceedings of the Amer. Math. Soc., 31 (1972) 228-231.

Lucas, W., Measuring Power in Weighted Voting Games, Case Studies in Applied Mathematics, Mathematical Association of America, Washington, 1976, pp. 42-106.

Lucas, W., Measuring power in weighted voting games, Chapter 9, in Political and Related Models, S. Brams, W. Lucas, and P. Straffin, Jr. (eds.), Springer-Verlag, New York, 1983, p. 183-238.

Saari, D., The ultimate of chaos resulting from weighted voting systems, Advances in Applied Math. 5 (1984) 286-308.

Shapley, L. and M. Shubik, A method for evaluating the distribution of power in a committee system, American Political Science Review, 48 (1954) 787-792.

Tannenbaum, P., Power in weighted voting systems, The Mathematica Journal 7 (1997) 59-63.

Taylor, A., Mathematics and Politics, Springer-Verlag, New York, l995.

Taylor, A. and W. Zwicker, A characterization of weighted voting, Pro. American Math. Soc. 115 (1992) 1089-1094.

Taylor, A. and W. Zwicker, Weighted voting, multicameral representation, and power, Games and Economic Behavior, 5 (1993) 170-181.

Taylor, A. and W. Zwicker, Simple Games and Magic Squares, J. Combinatorial Theory, ser. A., 71 (1995) 67-88.

Taylor, A. and W. Zwicker, Quasi-weightings, trading, and desirability relations in simple games, Games and Economic Behavior 16 (1996) 331-346.

Taylor, A. and W. Zwicker, Simple Games, Princeton U. Press, Princeton, 1999.

Tong, Z. and R. Kain, Vote assignments in weighted voting mechanisms, IEEE Transactions on Computers 40 (1991) 664-667.

Walther, E., An analysis of weighted voting systems using the Banzhaf value, Master of Science Thesis, School of Operatons Research and Industrial Engineering, Cornell University, Ithaca, 1977.


This work was prepared with partial support from the National Science Foundation (Grant Number: DUE 9555401) to the Long Island Consortium for Interconnected Learning (administered by SUNY at Stony Brook, Alan Tucker, Director).

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