{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T04:03:40Z","timestamp":1768968220448,"version":"3.49.0"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T00:00:00Z","timestamp":1743552000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T00:00:00Z","timestamp":1743552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Luiss University"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soc Choice Welf"],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We present an axiomatic study of various solutions to the social ranking problem, where a solution links any ranking of coalitions of players to a binary relation between individual players. We focus on solutions that align with the desirability relation, asserting that player\n                    <jats:italic>i<\/jats:italic>\n                    is more desirable than player\n                    <jats:italic>j<\/jats:italic>\n                    if any coalition including\n                    <jats:italic>i<\/jats:italic>\n                    but not\n                    <jats:italic>j<\/jats:italic>\n                    ranks higher than the corresponding coalition formed by replacing\n                    <jats:italic>i<\/jats:italic>\n                    with\n                    <jats:italic>j<\/jats:italic>\n                    . Unlike previous characterizations, our study highlights the central role of the desirability property as a foundational axiom in the characterization of five solutions from the related literature:\n                    <jats:italic>Ceteris Paribus<\/jats:italic>\n                    majority, lexicographic excellence and its dual,\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$L^{(1)}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    solution and its dual. Our main results reveal additional similarities among these five solutions and emphasize the essential features that should be considered when selecting the most appropriate solution for a given scenario. A practical application involving a bicameral legislature is also presented.\n                  <\/jats:p>","DOI":"10.1007\/s00355-025-01590-1","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T03:47:27Z","timestamp":1743738447000},"page":"721-763","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Desirability and social ranking"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5177-8176","authenticated-orcid":false,"given":"Michele","family":"Aleandri","sequence":"first","affiliation":[]},{"given":"Felix","family":"Fritz","sequence":"additional","affiliation":[]},{"given":"Stefano","family":"Moretti","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,2]]},"reference":[{"issue":"2","key":"1590_CR1","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1007\/s10479-021-04199-6","volume":"318","author":"M Aleandri","year":"2022","unstructured":"Aleandri M, Dall\u2019Aglio M, Fragnelli V, Moretti S (2022) Minimal winning coalitions and orders of criticality. Ann Oper Res 318(2):787\u2013803","journal-title":"Ann Oper Res"},{"key":"1590_CR2","doi-asserted-by":"crossref","unstructured":"Aleandri M, Fragnelli V, Moretti S (2023). In: Leroch MA, Rupp F (eds) Lexicographic ranking based on minimal winning coalitions. Springer, Cham, pp 239\u2013256","DOI":"10.1007\/978-3-031-23015-8_13"},{"issue":"4","key":"1590_CR3","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1007\/s00355-021-01340-z","volume":"57","author":"E Algaba","year":"2021","unstructured":"Algaba E, Moretti S, R\u00e9mila E, Solal P (2021) Lexicographic solutions for coalitional rankings. Soc Choice Welf 57(4):817\u2013849","journal-title":"Soc Choice Welf"},{"key":"1590_CR4","doi-asserted-by":"crossref","unstructured":"Allouche T, Escoffier B, Moretti S, Ozturk M (2021) Social ranking manipulability for the cp-majority, Banzhaf and lexicographic excellence solutions. In: Bessiere C (ed) 29th International joint conference on artificial intelligence (IJCAI-PRICAI-20), Yokohama, Japan, pp 17\u201323","DOI":"10.24963\/ijcai.2020\/3"},{"issue":"4","key":"1590_CR5","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1007\/s00355-018-1161-1","volume":"52","author":"G Bernardi","year":"2019","unstructured":"Bernardi G, Lucchetti R, Moretti S (2019) Ranking objects from a preference relation over their subsets. Soc Choice Welf 52(4):589\u2013606","journal-title":"Soc Choice Welf"},{"issue":"2","key":"1590_CR6","first-page":"139","volume":"32","author":"F Carreras","year":"1996","unstructured":"Carreras F, Freixas J (1996) Complete simple games. Math. Soc Sci 32(2):139\u2013155","journal-title":"Soc Sci"},{"issue":"2","key":"1590_CR7","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.mathsocsci.2007.08.004","volume":"55","author":"F Carreras","year":"2008","unstructured":"Carreras F, Freixas J (2008) On ordinal equivalence of power measures given by regular semivalues. Math Soc Sci 55(2):221\u2013234","journal-title":"Math Soc Sci"},{"key":"1590_CR8","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/s11238-014-9445-0","volume":"78","author":"S Courtin","year":"2015","unstructured":"Courtin S, Tchantcho B (2015) A note on the ordinal equivalence of power indices in games with coalition structure. Theory Decis 78:617\u2013628","journal-title":"Theory Decis"},{"key":"1590_CR9","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/BF01753239","volume":"7","author":"J Deegan","year":"1978","unstructured":"Deegan J, Packel EW (1978) A new index of power for simple n-person games. Int J Game Theory 7:113\u2013123","journal-title":"Int J Game Theory"},{"key":"1590_CR10","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1023\/A:1024158301610","volume":"53","author":"L Diffo Lambo","year":"2002","unstructured":"Diffo Lambo L, Moulen J (2002) Ordinal equivalence of power notions in voting games. Theory Decis 53:313\u2013325","journal-title":"Theory Decis"},{"issue":"1","key":"1590_CR11","doi-asserted-by":"publisher","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. Ann Oper Res 137(1):45\u201366","journal-title":"Ann Oper Res"},{"issue":"2","key":"1590_CR12","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.dss.2003.10.006","volume":"39","author":"J Freixas","year":"2005","unstructured":"Freixas J (2005) The Shapley\u2013Shubik power index for games with several levels of approval in the input and output. Decis Support Syst 39(2):185\u2013195","journal-title":"Decis Support Syst"},{"issue":"2","key":"1590_CR13","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1016\/j.ejor.2007.03.050","volume":"188","author":"J Freixas","year":"2008","unstructured":"Freixas J, Puente MA (2008) Dimension of complete simple games with minimum. Eur J Oper Res 188(2):555\u2013568","journal-title":"Eur J Oper Res"},{"key":"1590_CR14","doi-asserted-by":"crossref","unstructured":"Fritz F, Staudacher J, Stefano M (2023) Socialranking: social ranking solutions for power relations on coalitions. R package version 1.1.0. https:\/\/CRAN.R-project.org\/package=socialranking","DOI":"10.32614\/CRAN.package.socialranking"},{"key":"1590_CR15","doi-asserted-by":"publisher","unstructured":"Haret A, Khani H, Moretti S, Ozturk M (2018) Ceteris paribus majority for social ranking. In: Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence (IJCAI-18), International Joint Conferences on Artificial Intelligence Organization, pp 303\u2013309. https:\/\/doi.org\/10.24963\/ijcai.2018\/42","DOI":"10.24963\/ijcai.2018\/42"},{"key":"1590_CR16","doi-asserted-by":"publisher","unstructured":"Holler MJ, Nurmi H (2013) Power, voting, and voting power: 30\u00a0years after. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-3-642-35929-3","DOI":"10.1007\/978-3-642-35929-3"},{"key":"1590_CR17","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1215\/S0012-7094-58-02537-7","volume":"25","author":"JR Isbell","year":"1958","unstructured":"Isbell JR (1958) A class of simple games. Duke Math J 25:423\u2013439","journal-title":"Duke Math J"},{"key":"1590_CR18","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.geb.2015.06.003","volume":"92","author":"D Karos","year":"2015","unstructured":"Karos D, Peters H (2015) Indirect control and power in mutual control structures. Games Econ Behav 92:150\u2013165","journal-title":"Games Econ Behav"},{"key":"1590_CR19","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/j.geb.2017.01.012","volume":"108","author":"D Karos","year":"2018","unstructured":"Karos D, Peters H (2018) Effectivity and power. Games Econ Behav 108:363\u2013378","journal-title":"Games Econ Behav"},{"issue":"2","key":"1590_CR20","doi-asserted-by":"publisher","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. Pac. J. Math. 18(2):289\u2013328","journal-title":"Pac. J. Math."},{"key":"1590_CR21","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s11238-017-9630-z","volume":"85","author":"M Musegaas","year":"2018","unstructured":"Musegaas M, Borm P, Quant M (2018) Three-valued simple games. Theory Decis 85:201\u2013224","journal-title":"Theory Decis"},{"key":"1590_CR22","doi-asserted-by":"crossref","unstructured":"Shapley LS (1953) A value for n-person games. In: H., K., A.W., T. (eds.) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307\u2013317","DOI":"10.1515\/9781400881970-018"},{"key":"1590_CR23","doi-asserted-by":"crossref","unstructured":"Suzuki T, Horita M (2021) Social ranking problem based on rankings of restricted coalitions. In: International conference on group decision and negotiation. Springer, Berlin, pp 55\u201367","DOI":"10.1007\/978-3-030-77208-6_5"},{"key":"1590_CR24","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/s00355-023-01502-1","volume":"62","author":"T Suzuki","year":"2024","unstructured":"Suzuki T, Horita M (2024) Consistent social ranking solutions. Soc Choice Welf 62:549\u2013569","journal-title":"Soc Choice Welf"},{"key":"1590_CR25","doi-asserted-by":"crossref","unstructured":"Taylor AD, Zwicker W (1999) Simple games: desirability relations, trading, pseudoweightings. Princeton University Press, JSTOR. http:\/\/www.jstor.org\/stable\/j.ctv18zhdsm. Accessed 18 Mar 2025","DOI":"10.1515\/9780691223896"},{"issue":"1","key":"1590_CR26","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1006\/game.1993.1009","volume":"5","author":"A Taylor","year":"1993","unstructured":"Taylor A, Zwicker W (1993) Weighted voting, multicameral representation, and power. Games Econ Behav 5(1):170\u2013181","journal-title":"Games Econ Behav"}],"container-title":["Social Choice and Welfare"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-025-01590-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00355-025-01590-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-025-01590-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T16:37:55Z","timestamp":1761323875000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00355-025-01590-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,2]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["1590"],"URL":"https:\/\/doi.org\/10.1007\/s00355-025-01590-1","relation":{},"ISSN":["0176-1714","1432-217X"],"issn-type":[{"value":"0176-1714","type":"print"},{"value":"1432-217X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,2]]},"assertion":[{"value":"23 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 April 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}