{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T09:09:57Z","timestamp":1762160997218},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,4,10]],"date-time":"2013-04-10T00:00:00Z","timestamp":1365552000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2014,4]]},"DOI":"10.1007\/s10479-013-1374-8","type":"journal-article","created":{"date-parts":[[2013,4,9]],"date-time":"2013-04-09T10:53:16Z","timestamp":1365504796000},"page":"215-230","source":"Crossref","is-referenced-by-count":5,"title":["Banzhaf index for multiple voting systems. An application to the European Union"],"prefix":"10.1007","volume":"215","author":[{"given":"Luisa","family":"Monroy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco R.","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,4,10]]},"reference":[{"key":"1374_CR1","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/S0165-4896(02)00086-0","volume":"46","author":"E. Algaba","year":"2003","unstructured":"Algaba, E., Bilbao, J. M., Fern\u00e1ndez, J. R., & L\u00f3pez, J. J. (2003). Computing power indices in weighted multiple majority games. Mathematical Social Sciences, 46, 63\u201380.","journal-title":"Mathematical Social Sciences"},{"key":"1374_CR2","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10479-005-2242-y","volume":"137","author":"J. M. Alonso-Mejide","year":"2005","unstructured":"Alonso-Mejide, J. M., & Bowles, C. (2005). Generating functions for coalitional power indices: an application to the IMF. Annals of Operations Research, 137, 21\u201344.","journal-title":"Annals of Operations Research"},{"key":"1374_CR3","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1023\/A:1018901306738","volume":"84","author":"R. Amer","year":"1998","unstructured":"Amer, R., Carreras, F., & Maga\u00f1a, M. (1998). Extension of values to games with multiple alternatives. Annals of Operations Research, 84, 63\u201378.","journal-title":"Annals of Operations Research"},{"key":"1374_CR4","first-page":"317","volume":"19","author":"J. Banzhaf","year":"1965","unstructured":"Banzhaf, J. (1965). Weighted voting doesn\u2019t work: a mathematical analysis. Rutgers Law Review, 19, 317\u2013343.","journal-title":"Rutgers Law Review"},{"key":"1374_CR5","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF01240129","volume":"22","author":"E. M. Bolger","year":"1993","unstructured":"Bolger, E. M. (1993). A value for games with n players and r alternatives. International Journal of Game Theory, 22, 319\u2013334.","journal-title":"International Journal of Game Theory"},{"key":"1374_CR6","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF00141101","volume":"7","author":"S. J. Brams","year":"1976","unstructured":"Brams, S. J., & Affuso, P. J. (1976). Power and size. A new paradox. Theory and Decision, 7, 29\u201356.","journal-title":"Theory and Decision"},{"key":"1374_CR7","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1287\/moor.4.2.99","volume":"4","author":"P. Dubey","year":"1979","unstructured":"Dubey, P., & Shapley, L. S. (1979). Mathematical properties of the Banzhaf index. Mathematics of Operations Research, 4, 99\u2013131.","journal-title":"Mathematics of Operations Research"},{"key":"1374_CR8","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/BF01263275","volume":"26","author":"D. S. Felsenthal","year":"1997","unstructured":"Felsenthal, D. S., & Machover, M. (1997). Ternary voting games. International Journal of Game Theory, 26, 335\u2013351.","journal-title":"International Journal of Game Theory"},{"key":"1374_CR9","doi-asserted-by":"crossref","DOI":"10.4337\/9781840647761","volume-title":"The measurement of voting power: theory and practice. Problems and paradoxes","author":"D. S. Felsenthal","year":"1998","unstructured":"Felsenthal, D. S., & Machover, M. (1998). The measurement of voting power: theory and practice. Problems and paradoxes. London: Edward Elgar."},{"key":"1374_CR10","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1023\/A:1016348001805","volume":"109","author":"J. R. Fern\u00e1ndez","year":"2002","unstructured":"Fern\u00e1ndez, J. R., Algaba, E., Bilbao, J. M., Jim\u00e9nez, A., Jim\u00e9nez, N., & L\u00f3pez, J. J. (2002). Generating functions for computing the Myerson value. Annals of Operations Research, 109, 143\u2013158.","journal-title":"Annals of Operations Research"},{"key":"1374_CR11","volume-title":"The theory of social choice","author":"P. C. Fishburn","year":"1973","unstructured":"Fishburn, P. C. (1973). The theory of social choice. Princeton: Princeton University Press."},{"key":"1374_CR12","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10479-005-2244-9","volume":"137","author":"J. Freixas","year":"2005","unstructured":"Freixas, J. (2005). Banzhaf measures for games with several levels of approval in the input and output. Annals of Operations Research, 137, 45\u201365.","journal-title":"Annals of Operations Research"},{"key":"1374_CR13","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s00355-003-0212-3","volume":"21","author":"J. Freixas","year":"2003","unstructured":"Freixas, J., & Zwicker, W. S. (2003). Weighted voting, abstention, and multiple levels of approval. Social Choice and Welfare, 21, 399\u2013431.","journal-title":"Social Choice and Welfare"},{"key":"1374_CR14","series-title":"SIAM monographs on discrete mathematics and applications","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719819","volume-title":"Evaluation and optimization of electoral systems","author":"P. Grilli\u00a0di\u00a0Cortona","year":"1999","unstructured":"Grilli\u00a0di\u00a0Cortona, P., Manzi, C., Pennisi, A., Ricca, F., & Simeone, B. (1999). SIAM monographs on discrete mathematics and applications. Evaluation and optimization of electoral systems. Philadelphia: SIAM."},{"key":"1374_CR15","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1006\/game.1993.1014","volume":"5","author":"C. R. Hsiao","year":"1993","unstructured":"Hsiao, C. R., & Raghavan, T. E. S. (1993). Shapley value for multichoice cooperative games, I. Games and Economic Behavior, 5, 240\u2013256.","journal-title":"Games and Economic Behavior"},{"key":"1374_CR16","first-page":"295","volume":"32","author":"L. Monroy","year":"2007","unstructured":"Monroy, L., & Fern\u00e1ndez, F. R. (2007). Weighted multi-criteria simple games and voting systems. Foundations of Computing and Decision Sciences, 32, 295\u2013313.","journal-title":"Foundations of Computing and Decision Sciences"},{"key":"1374_CR17","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1016\/j.amc.2009.07.011","volume":"215","author":"L. Monroy","year":"2009","unstructured":"Monroy, L., & Fern\u00e1ndez, F. R. (2009). A general model for voting systems with multiple alternatives. Applied Mathematics and Computation, 215, 1537\u20131547.","journal-title":"Applied Mathematics and Computation"},{"key":"1374_CR18","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.ejor.2010.08.013","volume":"209","author":"L. Monroy","year":"2011","unstructured":"Monroy, L., & Fern\u00e1ndez, F. R. (2011). The Shapley\u2013Shubik index for multi-criteria simple games. European Journal of Operational Research, 209, 122\u2013128.","journal-title":"European Journal of Operational Research"},{"key":"1374_CR19","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s11238-010-9211-x","volume":"70","author":"R. Pongou","year":"2011","unstructured":"Pongou, R., Tchantcho, B., & Diffo Lambo, L. (2011). Political influence in multi-choice institutions: cyclicity, anonymity and transitivity. Theory and Decision, 70, 157\u2013178.","journal-title":"Theory and Decision"},{"key":"1374_CR20","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/0022-0531(80)90002-2","volume":"23","author":"A. Rubinstein","year":"1980","unstructured":"Rubinstein, A. (1980). Stability of decision systems under majority rule. Journal of Economic Theory, 23, 150\u2013159.","journal-title":"Journal of Economic Theory"},{"key":"1374_CR21","doi-asserted-by":"crossref","first-page":"787","DOI":"10.2307\/1951053","volume":"48","author":"L. S. Shapley","year":"1954","unstructured":"Shapley, L. S., & Shubik, M. (1954). A method for evaluating the distribution of power in a committee system. The American Political Science Review, 48, 787\u2013792.","journal-title":"The American Political Science Review"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-013-1374-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-013-1374-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-013-1374-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T18:09:42Z","timestamp":1559153382000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-013-1374-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,10]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,4]]}},"alternative-id":["1374"],"URL":"https:\/\/doi.org\/10.1007\/s10479-013-1374-8","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,10]]}}}