PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Weighted multi-criteria simple games and voting systems

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Multi-criteria simple games provide mathematical models for describing and analyzing group decision problems when the decision makers consider multiple qualitative criteria simultaneously. Voting systems and related social choice situations may be modelled as multi-criteria simple games. The goal of this paper is to propose a generalization of the notion of weighted simple games within this context. The basic concepts and the model are first introduced. Two different weighted representations for a multi-criteria simple game is established and its dimension is defined. Furthermore, we provide an extension of the classic Theorem of Taylor and Zwicker for these types of games, which permits both, the weighted representation of a multi-criteria simple game and a bound of its dimension to be obtained.
Rocznik
Strony
295--313
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Departamento de Economia Aplicada III. Facultad de Ciencias Economicias y Empresariales, Universidad de Sevilla. Avda. Ramon y Cajal 1, 41018-Sevilla, Spain
Bibliografia
  • [1] Balinski M.L., Young H.P., Fair Representation. Yale University press. New Haven, 1982.
  • [2] Bergstresser K., Yu P.L.. Domination structures and multicriteria problem in n-person games, Theory and Decision 8, 1977. 5-48.
  • [3] Blackwell D.. An analog of the minimax theorem for vector payoff. Pacific Journal of Mathematics 6, 1956, 1-8.
  • [4] Brams S., Affuso P., Mac Kilgore D., Presidential power: a game-theoretic analysis. In: in Bruce P.. Harrington C., and King G. (eds.) The Presidency in American Politics , 1989, 55-74.
  • [5] Borm P., Vermeulen D., Voonicveld M., The structure of the set of equilibria for two person multicriteria games, European Journal of Operational Research 148, 2003, 480-493.
  • [6] Corley S.G., Games with vector payoffs. Journal of Optimization Theory and Applications, 47, 1985, 463-475.
  • [7] Fernandez F.R. and Puerto J.. Vector linear programming in zero-sum multi-criteria matrix games. Journal of Optimization Theory and Applications, 89, 1996. 115-127.
  • [8] Fernandez F.R., Monroy L.. Puerto J., Multicriteria goal games. Journal of Optimization Theory and Applications 99, 1998. 403-421.
  • [9] Fernandez F.R., Hinojosa M., Puerto J., Core solutions in vector-valued games, Journal of Optimization Theory and Applications. 112. 2002. 331-360.
  • [10] Ghose D., Solution concepts in continuous-kernel multicriteria games. Journal of Optimization Theory and Applications. 69. 1991.
  • [11] Ghose D.B., Prasad U.R., Solution concepts in two-person multicriteria games. Journal of Optimization Theory and Applications 63, 1989. 167-189.
  • [12] Hinojosa M.A., Marmol A.M.. Monroy L.. Generalized maxmin solutions in multicriteria bargaining. Annals of Operations Research 137. 2005. 243-255.
  • [13] Krus L.. Bronisz P.. Solution concepts in multicriteria coperative games without side payment. In: J. Dolezal and J. Fidler (eds.) System Modelling and Optimization. Chapman and Hall. 1996.
  • [14] Marmol A.M., Monroy L., Rubiales V.. An equitable solution for multicriteria bargaining games. European Journal of Operational Research, 177. 1523-1534.
  • [15] Monroy L., Fernandez F.R., Multi-criteria simple games, acepted in V. Barichard. M. Ehrgott. X. Gandibleux and V. T'kindt (eds.), Lecture Notes in Economics and Mathematical Systems. Springer-Verlag , 2007.
  • [16] Nurmi H., Comparing Voting Systems. Rcidel 1987.
  • [17] Owen G.. Game Theory, 3rd. edition, Academic Pres. San Diego, 1995.
  • [18] Rodriguez. J.. Juegos simples vectoriales, PhD Thesis, Dpto. Estadistica e Inves-tigación Operativa. Universidad de Sevilla. Spain, 2004.
  • [19] Taylor A.D., Mathematics and Politics: Strategy, Voting, Power and Proof. Springer-Verlag, Xew York, 1995.
  • [20] Taylor A.D., Zwicker W.. A characterization of weighted voting, Proceedings of the American Mathematical Society, 115, 4, 1992, 1089-1094.
  • [21] Taylor A.D., Zwicker W., Weighted voting, multicameral representation, and power. Games and Economics Behavior, 5. 1993, 170-181.
  • [22] Taylor A.D., Zwicker W., Simple Games: Desirability Relations, Trading and Pseuweigthing, Princetons University Press. 1999.
  • [23] Wierzbicki A.P., Multiple criteria games: theory and applications. IIASA Working paper WP-92-080, 1992.
  • [24] Young H.P., Optimal voting rules, The Journal of Economic Perspec-&ves9,l,1995, 51-64.
  • [25] Zeleny M., Games with multiple payoffs, International Journal of Game Theory 4, 1976,179-191.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP1-0081-0051
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.