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Comparing two ways of measuring the power of party members in simple majority voting games

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EN
Abstrakty
EN
We examine two approaches to the problem of measuring the voting power of individuals in a voting body with an a priori coalition structure by means of the Shapley-Shubik index. In order to analyze this question we apply games with a priori unions and composite games. We compare these two approaches basing on voting games with 100 voters and different coalition structures and present our conclusions.
Rocznik
Strony
1189--1208
Opis fizyczny
Bibliogr. 20 poz., wykr.
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autor
Bibliografia
  • Albizuri, M.J. (2001) An Axiomatization of the Modified Banzhaf-Coleman Index. International Journal of Game Theory, 30, 167-176.
  • Banzhaf, J.F. (1965) Weighted Voting Doesn’t Work: a Mathematical Analysis. Rutgers Law Review, 19, 317-343.
  • Coleman, J.S. (1964) Introduction to Mathematical Sociology. Free Press of Glencoe, N.Y.
  • Dubey, P. (1975) On the Uniqueness of the Shapley Value. International Journal of Game Theory, 4, 131-139.
  • Ekes, M. (2006) Two Types of the Banzhaf – Coleman Index in Games with a priori Unions. Roczniki Kolegium Analiz Ekonomicznych SGH, 15, 31-45.
  • Felsenthal, D.S. and Machover, M. (1998) The Measurement of Voting Power. Theory and Practice, Problems and Paradoxes. Edward Elgar Publishing, Cheltenham.
  • Hart, S. and Kurz, M. (1983) On the Endogenous Formation of Coalitions. Econometrica, 51, 1295-1313.
  • Laruelle, A. and Valenciano, F. (2004) On the Meaning of Owen-Banzhaf Coalitional Value in Voting Situations. Theory and Decision, 56, 113-123.
  • Leech, D. and Leech, R. (2006) Voting Power and Voting Blocs. Public Choice, 127, 285-303.
  • Malawski, M. (2004) „Counting” Power Indices forGames witha prioriUnions. Theory and Decisions, 56, 125-140.
  • Owen, G. (1964) Solutions of Compound Simple Games. Ann. Math. Study 52, M. Dresher, L.S. Shapley and A. W. Tucker, eds., 307-317.
  • Owen, G. (1977) Values of Games with a priori Unions. In: R. Henn and O. Moschlin, eds., Essays in Honour of Oskar Morgenstern. Springer-Verlag, New York, 76-88.
  • Owen, G. (1978) Characterization of the Banzhaf-Coleman Index. SIAM Journal of Applied Math., 35, 315-327.
  • Owen, G. (1981) Modification of the Banzhaf-Coleman Index for Games with a priori Unions. In: M. J. Holler, ed., Power, Voting and Voting Power. Physica-Verlag, Würzburg, 232-238.
  • Penrose, L.S. (1946) The Elementary Statistics of Majority Voting. Journal of the Royal Statistical Society, 109, 53-57.
  • 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 (Annals of Mathematics Studies 28). Princeton University Press, 307-317.
  • Shapley, L.S. and Shubik, M. (1954) A Method for Evaluating the Distributions of Power in a Committee System. American Political Science Review, 48, 787-792.
  • Shapley, L.S. and Milnor, J.W. (1978) Values of Large Games II: Oceanic Games. Mathematics of Operations Research, 3, 290-307.
  • Sosnowska, H. (2003) Jak różnią się indeksy siły? (How do the power indices differ?, in Polish). Opere et Studio pro Oeconomia 1, Wyższa Szkoła Handlu i Finansów Międzynarodowych, Warszawa, 93-103.
  • Young, H.P. (1985) Monotonic Solutions of Cooperative Games. International Journal of Game Theory 14, 65-72.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BATC-0009-0031
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