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Two variations of the Public Good Index for games with a priori unions

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EN
Abstrakty
EN
This paper introduces two variations of the Public Good Index (Holler, 1982) for games with a priori unions. The first one stresses the public good property which suggests that all members of a winning coalition derive equal power. The second variation follows earlier work on the integration of a priori unions (Owen, 1977 and 1982) and refers to essential subsets of an a priori union when allocating power shares. Axiomatic characterizations of both indices are discussed. Numerical examples, one of them taken from a political setting, illustrate the new power indices presented in this paper.
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Strony
839--855
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Department of Statistics and Operations Research, University of Santiago de Compostela, Spain
Bibliografia
  • ALBIZURI, M.J. (2001) An axiomatization of the modified Banzhaf-Coleman index. International Journal of Game Theory 30, 167-176.
  • ALONSO-MEIJIDE, J.M. and FIESTRAS-JANEIRO, M.G. (2002) Modification of the Banzhaf value for games with a coalition structure. Annals of Operations Research 109, 213-227.
  • ALONSO-MEIJIDE, J.M. and BOWLES, C. (2005) Generating functions for coalitional power indices: an application to the IMF. Annals of Operations Research 137, 21-44.
  • ALONSO-MEIJIDE, J.M., CARRERAS, F. and FIESTRAS-JANEIRO, M.G. (2005) The multilinear extension and the symmetric coalition Banzhaf value. Theory and Decision 59, 111-126.
  • ALONSO-MEIJIDE, J.M., CARRERAS, F., FIESTRAS-JANEIRO, M.G. and OWEN, G. (2007) A comparative axiomatic characterization of the Banzhaf-Owen coalitional value. Decision Support Systems 43, 701-712.
  • ALONSO-MEIJIDE, J.M., CASAS-MÉNDEZ, B., HOLLER, M.J. and LORENZO-FREIRE, S. (2008) Computing power indices: multilinear extensions and new characterizations. European Journal of Operational Research 188, 540-554.
  • ALONSO-MEIJIDE, J.M., CASAS-MÉNDEZ, B., FIESTRAS-JANEIRO, M.G. and HOLLER, M.J. (2009) The Deegan-Packel index for simple games with a priori unions. Quality & Quantity (DOI 10.1007/S11135-009-9306-Z).
  • AMER, R., CARRERAS, F. and GIMÉNEZ, J.M. (2002) The modified Banzhaf value for games with a coalition structure: an axiomatic characterization. Mathematical Social Sciences 43, 45-54.
  • AUMANN, R. J. and DRÈZE, J.H. (1974) Cooperative games with coalition structure. International Journal of Game Theory 3, 217-237.
  • AUMANN, R. (1977) Game theory. In: J. Eatwell, M. Milgate and P. Newman, eds., The New Palgrave: a Dictionary of Economics, 2. Macmillan, 460-482.
  • BANZHAF, J.F. (1965) Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review 19, 317-343.
  • BRUECKNER, M. (2002) Extended probabilistic characterization of power indices. Homo Oeconomicus 19, 373-386.
  • CARRERAS, F. and MAGAÑA, A. (1994) The multilinear extension and the modified Banzhaf-Coleman index. Mathematical Social Sciences 28, 215-222.
  • CARRERAS, F., LLONGUERAS, D. and PUENTE, A. (2007) Partnerships in politics: a case study. Homo Oeconomicus 24, 469-484.
  • COLEMAN, J.S. (1971) Control of collectivities and the power of a collectivity to act. In: B. Lieberman, ed., Social Choice. Gordon and Breach, 269-300.
  • DEEGAN, J. and PACKEL, E.W. (1978) A new index of power for simple n-person games. International Journal of Game Theory 7, 113-123.
  • FELSENTHAL, D.S. and MACHOVER, M. (1998) The measurement of voting power: theory and practice, problems and paradoxes. Edward Elgar.
  • HOLLER, M.J. (1978) A prior party power and government formation. Munich Social Science Review 4, 25-41.
  • HOLLER, M.J. (1982) Forming coalitions and measuring voting power. Political Studies 30, 262-271.
  • HOLLER, M.J. and LI, X. (1995) From public good index to public value: An axiomatic approach and generalization. Control and Cybernetics 24, 257-270.
  • HOLLER, M.J. and NOHN, A. (2009) The Public Good Index with threats in a priori unions. Essays in Honor of Hannu Nurmi, Vol. 1, Homo Oeconomicus 26, 393-401.
  • HOLLER, M.J. and PACKEL, E.W. (1983) Power, luck and the right index. Journal of Economics 43, 21-29.
  • JOHNSTON, R.J. (1978) On the measurement of power: some reaction to Laver. Environment and Planning A 10, 907-914.
  • OWEN, G. (1972) Multilinear extensions of games. Management Science 18, 64-79.
  • OWEN, G. (1977) Values of games with a priori unions. In: R. Henn and O. Moeschlin, eds., Mathematical Economics and Game Theory. Springer Verlag, 76-88.
  • OWEN, G. (1982) Modification of the Banzhaf-Coleman index for games with a priori unions. In: M.J. Holler, ed., Power, Voting and Voting Power. Physica-Verlag, 232-238.
  • OWEN, G. and WINTER, E. (1992) Multilinear extensions and the coalition value. Games and Economic Behavior 4, 582-587.
  • PELEG, B. and SUDHÖLTER, P. (2003) Introduction to the Theory of Cooperative Games. Kluwer Academic Publisher.
  • SHAPLEY, L.S. (1953) A value for n-person games. Annals of Mathematics Studies 28, 307-318.
  • SHAPLEY, L.S. and SHUBIK, M. (1954) A method for evaluating the distribution of power in a committee system. American Political Science Review 48, 787-792.
  • TURNOVEC, F. (2011) Fair voting rules in committees, strict proportional power and optimal quota. Essays in Honor of Hannu Nurmi, Vol. 2, Homo Oeconomicus 27 (forthcoming).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0055-0032
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