{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T07:00:55Z","timestamp":1768892455699,"version":"3.49.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,9,24]],"date-time":"2008-09-24T00:00:00Z","timestamp":1222214400000},"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":[[2009,2]]},"DOI":"10.1007\/s10479-008-0422-2","type":"journal-article","created":{"date-parts":[[2008,9,23]],"date-time":"2008-09-23T15:52:00Z","timestamp":1222185120000},"page":"243-260","source":"Crossref","is-referenced-by-count":35,"title":["On the existence of a minimum integer representation for\u00a0weighted voting systems"],"prefix":"10.1007","volume":"166","author":[{"given":"Josep","family":"Freixas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xavier","family":"Molinero","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,9,24]]},"reference":[{"key":"422_CR1","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1137\/S0895480197326048","volume":"16","author":"V. Bohosian","year":"2003","unstructured":"Bohosian, V., & Bruck, J. (2003). Algebraic techniques for constructing minimal weights threshold functions. SIAM Journal on Discrete Mathematics, 16, 114\u2013126.","journal-title":"SIAM Journal on Discrete Mathematics"},{"key":"422_CR2","doi-asserted-by":"crossref","first-page":"831","DOI":"10.2307\/1955105","volume":"72","author":"S. J. Brams","year":"1976","unstructured":"Brams, S. J., & Fishburn, P. C. (1976). Approval voting. American Political Science Review, 72, 831\u2013847.","journal-title":"American Political Science Review"},{"key":"422_CR3","first-page":"104","volume-title":"LNCS: ISA\u201991 Algorithms","author":"E. Boros","year":"1991","unstructured":"Boros, E., Hammer, P. L., Ibaraki, T., & Kawakawi, K. (1991). Identifying 2-monotonic positive boolean functions in polynomial time. In W. L. Hsu & R. C. T. Lee (Eds.), LNCS: ISA\u201991 Algorithms (Vol. 557, pp. 104\u2013115). Berlin: Springer."},{"key":"422_CR4","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1137\/S0097539793269089","volume":"26","author":"E. Boros","year":"1997","unstructured":"Boros, E., Hammer, P. L., Ibaraki, T., & Kawakawi, K. (1997). Polynomial time recognition of 2-monotonic positive functions given by an oracle. SIAM Journal of Computing, 26, 93\u2013109.","journal-title":"SIAM Journal of Computing"},{"key":"422_CR5","doi-asserted-by":"crossref","first-page":"80","DOI":"10.2307\/2321942","volume":"80","author":"S. J. Brams Jr.","year":"1979","unstructured":"Brams, S. J., Jr., & Straffin, P.D. (1979). Prisoners\u2019 dilemma and the professional sports drafts. American Mathematical Monthly, 80, 80\u201388.","journal-title":"American Mathematical Monthly"},{"key":"422_CR6","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0165-4896(96)00815-3","volume":"32","author":"F. Carreras","year":"1996","unstructured":"Carreras, F., & Freixas, J. (1996). Complete simple games. Mathematical Social Sciences, 32, 139\u2013155.","journal-title":"Mathematical Social Sciences"},{"key":"422_CR7","volume-title":"Linear programming","author":"V. Chav\u00e1tal","year":"1983","unstructured":"Chav\u00e1tal, V. (1983). Linear programming. New York: Freeman."},{"key":"422_CR8","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 power index. Mathematics of Operations Research, 4, 99\u2013131.","journal-title":"Mathematics of Operations Research"},{"key":"422_CR9","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1287\/mnsc.16.3.179","volume":"16","author":"P. C. Fishburn","year":"1969","unstructured":"Fishburn, P. C. (1969). Preference, summation, and social welfare functions. Management Science, 16, 179\u2013186.","journal-title":"Management Science"},{"key":"422_CR10","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":"422_CR11","doi-asserted-by":"crossref","unstructured":"Freixas, J., & Molinero, X. (2008, accepted). Simple games and weighted games: a theoretical and computational viewpoint. Discrete Applied Mathematics.","DOI":"10.1016\/j.dam.2008.09.009"},{"key":"422_CR12","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":"422_CR13","unstructured":"Glpk (gnu linear programming kit) package. (2005). URL: http:\/\/www.gnu.org\/software\/glpk\/ ."},{"key":"422_CR14","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1137\/S089548019732787X","volume":"13","author":"P. L. Hammer","year":"2000","unstructured":"Hammer, P. L., Kogan, A., & Rothblum, U. G. (2000). Evaluation, strength and relevance of boolean functions. SIAM Journal on Discrete Mathematics, 13, 302\u2013312.","journal-title":"SIAM Journal on Discrete Mathematics"},{"key":"422_CR15","volume-title":"Threshold logic","author":"S. T. Hu","year":"1965","unstructured":"Hu, S. T. (1965). Threshold logic. USA: Univ. of California Press."},{"key":"422_CR16","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1215\/S0012-7094-58-02537-7","volume":"25","author":"J. R. Isbell","year":"1958","unstructured":"Isbell, J. R. (1958). A class of simple games. Duke Mathematics Journal, 25, 423\u2013439.","journal-title":"Duke Mathematics Journal"},{"key":"422_CR17","doi-asserted-by":"crossref","first-page":"21","DOI":"10.2307\/2002191","volume":"13","author":"J. R. Isbell","year":"1959","unstructured":"Isbell, J. R. (1959). On the enumeration of majority games. Mathematical Tables and Other Aids to Computation, 13, 21\u201328.","journal-title":"Mathematical Tables and Other Aids to Computation"},{"key":"422_CR18","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01415753","volume":"42","author":"I. Krohn","year":"1995","unstructured":"Krohn, I., & Sudh\u00f6lter, P. (1995). Directed and weighted majority games. ZOR-Mathematical Methods of Operations Research, 42, 189\u2013216.","journal-title":"ZOR-Mathematical Methods of Operations Research"},{"key":"422_CR19","unstructured":"Maple. (2005). URL: http:\/\/www.maplesoft.com\/ ."},{"key":"422_CR20","unstructured":"Matlab. (2005). URL: http:\/\/www.mathworks.com\/products\/matlab\/ ."},{"key":"422_CR21","doi-asserted-by":"crossref","first-page":"289","DOI":"10.2140\/pjm.1966.18.289","volume":"18","author":"M. Maschler","year":"1966","unstructured":"Maschler, M., & Peleg, B. (1966). A characterization, existence proof, and dimension bounds for the kernel of a game. Pacific Journal of Mathematics, 18, 289\u2013328.","journal-title":"Pacific Journal of Mathematics"},{"key":"422_CR22","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1090\/S0025-5718-62-99195-0","volume":"16","author":"S. Muroga","year":"1962","unstructured":"Muroga, S., Toda, I., & Kondo, M. (1962). Majority decision functions of up to six variables. Mathematics of Computation, 16, 459\u2013472.","journal-title":"Mathematics of Computation"},{"key":"422_CR23","volume-title":"Threshold logic and its applications","author":"S. Muroga","year":"1971","unstructured":"Muroga, S. (1971). Threshold logic and its applications. New York: Wiley."},{"key":"422_CR24","volume-title":"Theory of games and economic behavior","author":"J. Neumann Von","year":"1944","unstructured":"Von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton: Princeton University Press."},{"key":"422_CR25","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/BF01282564","volume":"45","author":"A. Ostmann","year":"1985","unstructured":"Ostmann, A. (1985). Decisions by players of comparable strength. Journal of Economics, 45, 267\u2013284.","journal-title":"Journal of Economics"},{"key":"422_CR26","volume-title":"Mathematical programming: structures and algorithms","author":"J. F. Shapiro","year":"1979","unstructured":"Shapiro, J. F. (1979). Mathematical programming: structures and algorithms. New York: Wiley."},{"key":"422_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-2512-6","volume-title":"Mathematics and politics","author":"A. D. Taylor","year":"1995","unstructured":"Taylor, A. D. (1995). Mathematics and politics. New York: Springer."},{"key":"422_CR28","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1090\/S0002-9939-1992-1092927-0","volume":"115","author":"A. D. Taylor","year":"1992","unstructured":"Taylor, A. D., & Zwicker, W. S. (1992). A characterization of weighted voting. Proceedings of the American Mathematical Society, 115, 1089\u20131094.","journal-title":"Proceedings of the American Mathematical Society"},{"key":"422_CR29","volume-title":"Simple games: desirability relations, trading, and pseudoweightings","author":"A. D. Taylor","year":"1999","unstructured":"Taylor, A. D., & Zwicker, W. S. (1999). Simple games: desirability relations, trading, and pseudoweightings. New Jersey: Princeton University Press."}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-008-0422-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-008-0422-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-008-0422-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T18:07:49Z","timestamp":1559153269000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-008-0422-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,24]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,2]]}},"alternative-id":["422"],"URL":"https:\/\/doi.org\/10.1007\/s10479-008-0422-2","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9,24]]}}}