Abstract
This work focuses on (j, 2) games in which there are several levels of approval in the input, i. e. games with n players, j ordered qualitative alternatives in the input level and 2 possible ordered quantitative alternatives in the output. When considering (j, 2) games, we extend the Public Good index (PGI), the Null Player Free index (NPFI) and the Shift index (SI) and provide full characterizations of these extensions.
Acknowledgements
The authors would like to thank this University for its hospitality. This work has also benefited from comments and encouragemen by a number of conference and seminar participants.The authors thank also ane anonymous reviewers and one associate Editor for their useful comments. This research was developed within the CoCoRICo-CoDEC research program (ANR-14-CE24-0007-02).
References
Alonso-Meijide, J. M., and J. Freixas. 2010. “A New Power Index Based on Minimal Winning Coalitions Without any Surplus.” Decision Support System 49: 70–76.10.1016/j.dss.2010.01.003Search in Google Scholar
Alonso-Meijide, J. M., B. Casas-Méndez, M. J. Holler, and S. Lorenzo-Freire. 2008. “Computing Power Indices: Multilinear Extensions and New Characterizations.” European Journal of Operational Research 188: 540–54.10.1016/j.ejor.2007.04.019Search in Google Scholar
Alonso-Meijide, J. M., B. Casas-Méndez, G. Fiestras-Janeiro, M. J. Holler, and A. Nohn. 2010. “Axiomatizations of Public Good Indices with a Priori Unions.” Social Choice and Welfare 35: 517–33.10.1007/s00355-010-0451-zSearch in Google Scholar
Alonso-Meijide, J. M., M. Álvarez-Mozos, F. Ferreira, and A. Pinto. 2011. “Two New Power Indices Based on Winning Coalitions.” Journal of Difference Equations and Applications 17: 1095–100.10.1080/10236190903200677Search in Google Scholar
Álvarez-Mozos, M. 2012. “Essays on Cooperative Games with Restricted Cooperative and Simple Games.” PhD Thesis, University of Santiago de Compostela, Spain.Search in Google Scholar
Andjiga, N., F. Chantreuil, and D. Lepelley. 2003. “La mesure du pouvoir de vote.” Mathematiques et Sciences Humaines 163: 111–45.10.4000/msh.2920Search in Google Scholar
Banzhaf, J. F. 1965. “Weighted Voting Doesn’t Work: A Mathematical Analysis.” Rutgers Law Review 19: 317–43.Search in Google Scholar
Barry, B. 1980. “Is it Better to be Powerful or Lucky: Part I and Part II. Political Studies 28: 183–94 and 338–52.10.1111/j.1467-9248.1980.tb01244.xSearch in Google Scholar
Courtin, S., Z. Nganmeni, and B. Tchantcho. 2016. “The Shapley-Shubik Power Index for Dichotomous Multi-type Games.” Theory and Decision 81: 413–26.10.1007/s11238-016-9541-4Search in Google Scholar
Courtin, S., Z. Nganmeni, and B. Tchantcho. 2017. “Dichotomous Multi-type Games with a Coalition Structure.” Mathematical Social Sciences 86: 9–17.10.1016/j.mathsocsci.2016.12.003Search in Google Scholar
Deegan, J., and E. W. Packel. 1978. “A New Index of Power for Simple n-Person Games.” International Journal of Game Theory 7: 113–23.10.1007/BF01753239Search in Google Scholar
Freixas, J. 2005a. “The Banzhaf Index for Games with Several Levels of Approval in the Input and Output.” Annals of Operations Research 137: 45–66.10.1007/s10479-005-2244-9Search in Google Scholar
Freixas, J. 2005b. “The Shapley Shubik Power Index for Games with Several Levels of Approval in the Input and Output.” Decision Support Systems 39: 185–95.10.1016/j.dss.2003.10.006Search in Google Scholar
Freixas, J., and W. S. Zwicker. 2003a. “Weighted Voting, Abstention, and Multiple Levels of Approval.” Social Choice and Welfare 21: 399–431.10.1007/s00355-003-0212-3Search in Google Scholar
Freixas, J., and W. S. Zwicker. 2003b. “Weighted Voting, Abstention, and Multiple Levels of Approval.” Social Choice and Welfare 21: 399–431.10.1007/s00355-003-0212-3Search in Google Scholar
M. J. Holler. 1982. “Forming Coalitions and Measuring Voting Power.” Political Studies 30: 262–71.10.1111/j.1467-9248.1982.tb00537.xSearch in Google Scholar
Holler, M. J., and E. W. Packel. 1983. “Power, Luck and the Right Index.” Journal of Economics 43: 21–29.10.1007/BF01283881Search in Google Scholar
Isbell, J. R. 1958. “A Class of Simple Games.” Duke Mathematical Journal 25: 423–39.10.1215/S0012-7094-58-02537-7Search in Google Scholar
Laruelle, A., and F. Valenciano. 2008. Voting and Collective Decision-Making, 1st ed. Cambridge: Cambridge University Press.10.1017/CBO9780511493553Search in Google Scholar
Pongou, R., B. Tchantcho, and L. Diffo Lambo. 2011. “Political Influence in Multi-choice Institutions: Cyclicity, Anonymity, and Transitivity.” Theory and Decision 70: 157–78.10.1007/s11238-010-9211-xSearch in Google Scholar
Pongou, R., B. Tchantcho, and L. Tedjeugang. 2014. “Power Theories for Multi-choice Organizations and Political Rules: Rank-order Equivalence.” Operations Research Perspectives 1: 42–49.10.1016/j.orp.2014.06.002Search in Google Scholar
Pongou, R., B. Tchantcho, J. S Zwicker, and N. Tedjeugang. 2017. “Properties of Ladder Tournaments.” European Journal of Operational Research 263: 203–13.10.1016/j.ejor.2017.03.082Search in Google Scholar
W. H. Riker. 1982. “Theory of Political Coalitions.” Journal Studies 30: 262–71.Search in Google Scholar
L. S. Shapley, and M. Shubik. 1954. “A Model for Evaluating the Distribution of Power in a Committee System.” Rutgers Law Review 48: 787–92.Search in Google Scholar
Tchantcho, B., L. Diffo Lambo, and R. Pongou. 2008. “Voters’ Power in Voting Games with Abstention: Influence Relation and Ordinal Equivalence of Power Theories.” Games and Economic Behavior 64: 335–50.10.1016/j.geb.2007.10.014Search in Google Scholar
Notes
This project was written while B. Tchantcho was visiting the University of Caen.
© 2019 Walter de Gruyter GmbH, Berlin/Boston
