A decisiveness index for simple games

European Journal of Operational Research

Volumn 163, Issue 2, 2005, Pages 370-387

  Carreras, Francesc ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Banzhaf index; Decisiveness; Power; Simple game; Voting

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; DECISION MAKING; OPERATIONS RESEARCH; PROBABILITY DISTRIBUTIONS; SET THEORY;

BANZHAF INDEX; DECISIVENESS; SIMPLE GAMES; VOTING;

GAME THEORY;

EID: 10044271007     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2003.06.041     Document Type: Article

References (32)

1. Banzhaf, J.F., 1965. Weigthed voting doesn't work: A mathematical analysis. Rutgers Law Review 19, 317-343.
2. Calvo, E., Santos, J.C., 1997. Potentials in cooperative TU-games. Mathematical Social Sciences 34, 175-190.
3. Carreras, F., Freixas, J., 1996. Complete simple games. Mathematical Social Sciences 32, 139-155.
4. Carreras, F., Freixas, J., 2000. A note on regular semivalues. International Game Theory Review 2, 345-352.
5. Coleman, J.S., 1971. Control of collectivities and the power of a collectivity to act. In: Lieberman, B. (Ed.), Social Choice. Gordon and Breach, New York, pp. 269-300.
6. Deegan, J., Packel, E.W., 1978. A new index of power for simple n-person games. International Journal of Game Theory 7, 113-123.
7. Dragan, I., 1996. New mathematical properties of the Banzhaf value. European Journal of Operations Research 95, 451-463.
8. Dubey, P., 1975a. Some results on values of finite and infinite games. Ph.D. Thesis. Cornell University, Ithaca, NY.
9. Dubey, P., 1975b. On the uniqueness of the Shapley value. International Journal of Game Theory 4, 131-139.
10. Dubey, P., Shapley, L.S., 1979. Mathematical properties of the Banzhaf power index. Mathematics of Operations Research 4, 99-131.
11. Felsenthal, D.S., Machover, M., 1998. The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes. Edward Elgar Publishers.
12. Feltkamp, V., 1995. Alternative axiomatic characterizations of the Shapley and Banzhaf values. International Journal of Game Theory 24, 179-186.
13. Gambarelli, G., 1994. Power indices for political and financial decision making: A review. Annals of Operations Research 51, 165-173.
14. Hart, S., Mas-Colell, A., 1988. The potential of the Shapley value. In: Roth, A.E. (Ed.), The Shapley Value: Essays in Honor of Lloyd S. Shapley. Cambridge University Press, pp. 127-137.
15. Hart, S., Mas-Colell, A., 1989. Potential, value and consistency. Econometrica 57, 589-614.
16. Hoede, C., Bakker, R., 1982. A theory of decisional power. Journal of Mathematical Sociology 8, 309-322.
17. Holler, M.J., 1982. Forming coalitions and measuring voting power. Political Studies 30, 262-271.
18. Holler, M.J., Packel, E.W., 1983. Power, luck and the right index. Journal of Economics 43, 21-29.
19. Johnston, R.J., 1978. On the measurement of power: Some reactions to Laver. Environment and Planning A 10, 907-914.
20. König, T., Bräuninger, T., 1998. The inclusiveness of European decision rules. Journal of Theoretical Politics 10, 125-142.
21. Laruelle, A., 2000. On the choice of a power index. Working Paper WP-AD 99-10 of the University of Alicante, Spain.
22. Lehrer, E., 1988. An axiomatization of the Banzhaf value. International Journal of Game Theory 17, 89-99.
23. Ordeshook, P., 1986. Game Theory and Political Theory: An Introduction. Cambridge University Press.
24. Owen, G., 1975. Multilinear extensions and the Banzhaf value. Naval Research Logistics Quarterly 22, 741-750.
25. Owen, G., 1978. Characterization of the Banzhaf-Coleman index. SIAM Journal of Applied Mathematics 35, 315-327.
26. Peleg, B., 1992. Voting by count and account. In: Selten, R. (Ed.), Rational Interaction. Essays in Honor of John C. Harsanyi. Springer-Verlag.
27. Roth, A.E. (Ed.), 1988. The Shapley value: Essays in Honor of Lloyd S. Shapley. Cambridge University Press.
28. Shapley, L.S., 1953. A value for n-person games. In: Kuhn, H.W., Tucker, A.W. (Eds.), Contributions to the Theory of Games II. Princeton University Press, pp. 307-317.
29. Shapley, L.S., 1962. Simple games: An outline of the descriptive theory. Behavioral Science 7, 59-66.
30. Shapley, L.S., Shubik, M., 1954. A method for evaluating the distribution of power in a committee system. American Political Science Review 48, 787-792.
31. Straffin, P.D., 1988. The Shapley-Shubik and Banzhaf power indices as probabilities. In: Roth, A.E. (Ed.), The Shapley value: Essays in honor of Lloyd S. Shapley. Cambridge University Press, pp. 71-81.
32. Taylor, A., 1995. Mathematics and Politics: Strategy, Voting, Power and Proof. Springer-Verlag.