{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T10:33:56Z","timestamp":1768300436171,"version":"3.49.0"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,4,15]],"date-time":"2023-04-15T00:00:00Z","timestamp":1681516800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,4,15]],"date-time":"2023-04-15T00:00:00Z","timestamp":1681516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["MTM2017-87197-C3-3-P"],"award-info":[{"award-number":["MTM2017-87197-C3-3-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eca, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["MTM2017-87197-C3-2-P"],"award-info":[{"award-number":["MTM2017-87197-C3-2-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010801","name":"Xunta de Galicia","doi-asserted-by":"publisher","award":["ED431C 2021\/24"],"award-info":[{"award-number":["ED431C 2021\/24"]}],"id":[{"id":"10.13039\/501100010801","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010801","name":"Xunta de Galicia","doi-asserted-by":"publisher","award":["ED431C 2020\/03"],"award-info":[{"award-number":["ED431C 2020\/03"]}],"id":[{"id":"10.13039\/501100010801","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2021-124030NB-C32"],"award-info":[{"award-number":["PID2021-124030NB-C32"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007225","name":"Ministry of Science and Technology","doi-asserted-by":"publisher","award":["PID2021-124030NB-C32"],"award-info":[{"award-number":["PID2021-124030NB-C32"]}],"id":[{"id":"10.13039\/100007225","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007225","name":"Ministry of Science and Technology","doi-asserted-by":"publisher","award":["PID2021-124030NB-C33"],"award-info":[{"award-number":["PID2021-124030NB-C33"]}],"id":[{"id":"10.13039\/100007225","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2024,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we introduce a notion of mergeable weighted majority games with the aim of providing the first characterization of the Colomer\u2013Mart\u00ednez power index (Colomer and Mart\u00ednez in J Theor Polit 7(1):41\u201363, 1995). Furthermore, we define and characterize a new power index for the family of weighted majority games that combines ideas of the Public Good (Holler in Polit Stud 30(2):262\u2013271, 1982) and Colomer\u2013Mart\u00ednez power indices. Finally, we analyze the National Assembly of Ecuador using these and some other well-known power indices.<\/jats:p>","DOI":"10.1007\/s10479-023-05340-3","type":"journal-article","created":{"date-parts":[[2023,4,15]],"date-time":"2023-04-15T09:02:07Z","timestamp":1681549327000},"page":"1373-1393","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Mergeable weighted majority games and characterizations of some power indices"],"prefix":"10.1007","volume":"336","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8553-536X","authenticated-orcid":false,"given":"Livino M.","family":"Armijos-Toro","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8723-1404","authenticated-orcid":false,"given":"Jos\u00e9 M.","family":"Alonso-Meijide","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4769-6119","authenticated-orcid":false,"given":"Manuel A.","family":"Mosquera","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,15]]},"reference":[{"key":"5340_CR1","doi-asserted-by":"crossref","unstructured":"Alonso-Meijide, J. M., Casas-M\u00e9ndez, B., & Fiestras-Janeiro, M. G. (2013). A review of some recent results on power indices. In M. J. Holler & H. Nurmi (Eds.), Power, voting, and voting power: 30 Years after (pp. 231\u2013245). Springer.","DOI":"10.1007\/978-3-642-35929-3_12"},{"key":"5340_CR2","first-page":"317","volume":"19","author":"JF Banzhaf","year":"1965","unstructured":"Banzhaf, J. F. (1965). Weighted voting does not work: A mathematical analysis. Rutgers Law Review, 19, 317\u2013343.","journal-title":"Rutgers Law Review"},{"issue":"4","key":"5340_CR3","first-page":"459","volume":"22","author":"R Barua","year":"2005","unstructured":"Barua, R., Chakravarty, S. R., & Roy, S. (2005). Measuring power in weighted majority games. Homo Oeconomicus, 22(4), 459\u2013486.","journal-title":"Homo Oeconomicus"},{"issue":"1","key":"5340_CR4","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1177\/0951692895007001003","volume":"7","author":"JM Colomer","year":"1995","unstructured":"Colomer, J. M., & Mart\u00ednez, F. (1995). The paradox of coalition trading. Journal of Theoretical Politics, 7(1), 41\u201363.","journal-title":"Journal of Theoretical Politics"},{"issue":"2","key":"5340_CR5","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/BF01753239","volume":"7","author":"J Deegan","year":"1978","unstructured":"Deegan, J., & Packel, E. W. (1978). A new index of power for simple $$n$$-person games. International Journal of Game Theory, 7(2), 113\u2013123.","journal-title":"International Journal of Game Theory"},{"issue":"2","key":"5340_CR6","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/BF01780630","volume":"4","author":"P Dubey","year":"1975","unstructured":"Dubey, P. (1975). On the uniqueness of the Shapley value. International Journal of Game Theory, 4(2), 131\u2013139.","journal-title":"International Journal of Game Theory"},{"issue":"2","key":"5340_CR7","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1111\/j.1467-9248.1982.tb00537.x","volume":"30","author":"MJ Holler","year":"1982","unstructured":"Holler, M. J. (1982). Forming coalitions and measuring voting power. Political Studies, 30(2), 262\u2013271.","journal-title":"Political Studies"},{"issue":"1","key":"5340_CR8","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/BF01283881","volume":"43","author":"MJ Holler","year":"1983","unstructured":"Holler, M. J., & Packel, E. W. (1983). Power, luck and the right index. Zeitschrift f\u00fcr National\u00f6konomie \/ Journal of Economics, 43(1), 21\u201329.","journal-title":"Zeitschrift f\u00fcr National\u00f6konomie \/ Journal of Economics"},{"issue":"1","key":"5340_CR9","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s41412-016-0002-7","volume":"33","author":"L\u00c1 K\u00f3czy","year":"2016","unstructured":"K\u00f3czy, L. \u00c1. (2016). Power indices when players can commit to reject coalitions. Homo Oeconomicus, 33(1), 77\u201391.","journal-title":"Homo Oeconomicus"},{"key":"5340_CR10","unstructured":"Laruelle, A. (1999). On the choice of a power index. Tech. Rep. WP-AD 99-10, Instituto Valenciano de Investigaciones Econ\u00f3micas."},{"key":"5340_CR11","first-page":"307","volume":"28","author":"LS Shapley","year":"1953","unstructured":"Shapley, L. S. (1953). A value for $$n$$-person games. Annals of Mathematics Studies, 28, 307\u2013317.","journal-title":"Annals of Mathematics Studies"},{"issue":"3","key":"5340_CR12","doi-asserted-by":"publisher","first-page":"787","DOI":"10.2307\/1951053","volume":"48","author":"LS Shapley","year":"1954","unstructured":"Shapley, L. S., & Shubik, M. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review, 48(3), 787\u2013792.","journal-title":"American Political Science Review"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-023-05340-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-023-05340-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-023-05340-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T16:14:31Z","timestamp":1715703271000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-023-05340-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,15]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["5340"],"URL":"https:\/\/doi.org\/10.1007\/s10479-023-05340-3","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,15]]},"assertion":[{"value":"4 April 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 April 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}