Abstract
In this paper we provide a generalized power index which gives a measurement of voting power in multi-candidate elections with weighted voting using preference ballots. We use the power index to compare the power of various players between an election using plurality and one using the Borda method. The power index is based upon the Banzhaf power index.
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Banzhaf JF III (1965) Weighted voting doesn't work: A mathematical analysis. Rutgers Law Rev 19: 317–343
Bolger EM (1983) The Banzhaf index for multicandidate presidential elections. SIAM J Algebraic Discrete Methods 4: 422–458
Bolger EM (1986) Power indices for multicandidate voting games. Int J Game Theory 14: 175–186
Bolger EM (1990) A characterization of an extension of the Banzhaf value to multicandidate voting games. SIAM J Discrete Math 3(4): 466–477
Cayley A (1891) On the analytical forms called trees. Collected Mathematical Papers, Cambridge University Press, Cambridge 4: 112–115
Even S (1973) Algorithmic Combinatorics. MacMillan, New York
Feld SL, Grofman B (1990) A theorem connecting Shapley-Owen power scores and the radius of the yolk in two dimensions. Soc Choice Welfare 7: 71–74
Gross OA (1962) Preferential arrangements. Amer Math Monthly 69: 4–8
MacMahon PA (1891) Yoke-chains and multipartite compositions in connexion with the analytical forms called trees. Proc London Math Soc 22: 330–346
Mor M, Fraenkel AS (1984) Cayley Permutations. Discrete Math 48: 101–112
Motzkin TS (1971) Sorting numbers for cylinders and other classification numbers. Proc Symp Pure Math Amer Math Soc, Providence, RI, pp 167–176
Rae DW (1969) Decision rules and individual values in constitutional choice. Amer Polit Science Rev 63: 40–56
Saari DG (1994) Geometry of Voting. Springer, Berlin (1994)
Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in a committee system. Amer Pol Sci Rev 48: 787–792
Straffin PD (1989) Spatial models of power and voting outcomes. In: Roberts F (ed.) Applications of combinatorics and graph theory to the biological and social sciences. Springer, Berlin pp 315–335
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Haunsperger, D.B., Melville, D.J. Voting power when using preference ballots. Soc Choice Welfare 13, 457–465 (1996). https://doi.org/10.1007/BF00182856
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DOI: https://doi.org/10.1007/BF00182856