{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T07:03:52Z","timestamp":1772607832211,"version":"3.50.1"},"reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Social Sciences"],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1016\/j.mathsocsci.2026.102515","type":"journal-article","created":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T00:24:02Z","timestamp":1770855842000},"page":"102515","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Between proportionnality and envy-freeness:\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e214\">\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:math>\n                    -proportionality"],"prefix":"10.1016","volume":"140","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9657-4209","authenticated-orcid":false,"given":"Guillaume","family":"Ch\u00e8ze","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.mathsocsci.2026.102515_b1","doi-asserted-by":"crossref","unstructured":"Aziz, H., Mackenzie, S., 2016. A discrete and bounded envy-free cake cutting protocol for any number of agents. In: IEEE 57th Annual Symposium on Foundations of Computer Science, FOCS 2016, 9-11 October 2016. pp. 416\u2013427.","DOI":"10.1109\/FOCS.2016.52"},{"issue":"11","key":"10.1016\/j.mathsocsci.2026.102515_b2","doi-asserted-by":"crossref","first-page":"3443","DOI":"10.1090\/S0002-9939-96-03476-4","article-title":"On the possibilities for partitioning a cake","volume":"124","author":"Barbanel","year":"1996","journal-title":"Proc. Amer. Math. Soc."},{"key":"10.1016\/j.mathsocsci.2026.102515_b3","series-title":"The Geometry of Efficient Fair Division","author":"Barbanel","year":"2005"},{"issue":"6","key":"10.1016\/j.mathsocsci.2026.102515_b4","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1080\/00029890.2009.11920966","article-title":"Cutting a pie is not a piece of cake","volume":"116","author":"Barbanel","year":"2009","journal-title":"Am. Math. Mon."},{"issue":"11","key":"10.1016\/j.mathsocsci.2026.102515_b5","first-page":"1314","article-title":"Better ways to cut a cake","volume":"53","author":"Brams","year":"2006","journal-title":"Notices Amer. Math. Soc."},{"issue":"1","key":"10.1016\/j.mathsocsci.2026.102515_b6","doi-asserted-by":"crossref","first-page":"35","DOI":"10.4169\/amer.math.monthly.120.01.035","article-title":"N-person cake-cutting: There may be no perfect division","volume":"120","author":"Brams","year":"2013","journal-title":"Am. Math. Mon."},{"issue":"1","key":"10.1016\/j.mathsocsci.2026.102515_b7","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/00029890.1995.11990526","article-title":"An envy-free cake division protocol","volume":"102","author":"Brams","year":"1995","journal-title":"Am. Math. Mon."},{"key":"10.1016\/j.mathsocsci.2026.102515_b8","series-title":"Fair division - from cake-cutting to dispute resolution","author":"Brams","year":"1996"},{"issue":"Supplement C","key":"10.1016\/j.mathsocsci.2026.102515_b9","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.ins.2012.11.024","article-title":"On the existence of equitable cake divisions","volume":"228","author":"Cechl\u00e1rov\u00e1","year":"2013","journal-title":"Inform. Sci."},{"key":"10.1016\/j.mathsocsci.2026.102515_b10","first-page":"3","article-title":"Issues in multiagent resource allocation","volume":"30","author":"Chevaleyre","year":"2006","journal-title":"INFORMATICA"},{"key":"10.1016\/j.mathsocsci.2026.102515_b11","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.mathsocsci.2017.03.006","article-title":"Existence of a simple and equitable fair division: A short proof","volume":"87","author":"Ch\u00e8ze","year":"2017","journal-title":"Math. Social Sci."},{"key":"10.1016\/j.mathsocsci.2026.102515_b12","doi-asserted-by":"crossref","unstructured":"Csercsik, D\u00e1vid, Sziklai, Bal\u00e1zs R., Imre, S\u00e1ndor, 2019. Cake-cutting approach for privacy-enhanced base station sharing in a linear model of user assignment. In: 2019 16th International Symposium on Wireless Communication Systems. ISWCS, pp. 618\u2013623.","DOI":"10.1109\/ISWCS.2019.8877192"},{"issue":"1","key":"10.1016\/j.mathsocsci.2026.102515_b13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2311357","article-title":"How to cut a cake fairly","volume":"68","author":"Dubins","year":"1961","journal-title":"Am. Math. Mon."},{"issue":"4","key":"10.1016\/j.mathsocsci.2026.102515_b14","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1145\/2000807.2000819","article-title":"Cake cutting really is not a piece of cake","volume":"7","author":"Edmonds","year":"2011","journal-title":"ACM Trans. Algorithms"},{"issue":"3","key":"10.1016\/j.mathsocsci.2026.102515_b15","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0166-218X(84)90005-2","article-title":"A note on cake cutting","volume":"7","author":"Even","year":"1984","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/j.mathsocsci.2026.102515_b16","first-page":"3356","article-title":"On connected strongly-proportional cake-cutting","volume":"392","author":"Jank\u00f3","year":"2024","journal-title":"ECAI 2024"},{"key":"10.1016\/j.mathsocsci.2026.102515_b17","doi-asserted-by":"crossref","unstructured":"Kash, I., Procaccia, A., Shah, N., 2013. No agent left behind: dynamic fair division of multiple resources. In: International Conference on Autonomous Agents and Multi-Agent Systems, AAMAS \u201913, Saint Paul, MN, USA, May 6-10, 2013. pp. 351\u2013358.","DOI":"10.65109\/MBLC7804"},{"key":"10.1016\/j.mathsocsci.2026.102515_b18","series-title":"On hierarchies of fairness notions in cake cutting: From proportionality to super envy-freeness","author":"Mehra","year":"2025"},{"issue":"8","key":"10.1016\/j.mathsocsci.2026.102515_b19","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1080\/00029890.2000.12005263","article-title":"On envy-free cake division","volume":"107","author":"Pikhurko","year":"2000","journal-title":"Am. Math. Mon."},{"key":"10.1016\/j.mathsocsci.2026.102515_b20","series-title":"Handbook of Computational Social Choice","article-title":"Cake cutting algorithms","author":"Procaccia","year":"2016"},{"key":"10.1016\/j.mathsocsci.2026.102515_b21","series-title":"Cake-cutting algorithms - be fair if you can","author":"Robertson","year":"1998"},{"key":"10.1016\/j.mathsocsci.2026.102515_b22","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1007\/s00355-019-01210-9","article-title":"Fair cake-cutting among families","volume":"53","author":"Segal-Halevi","year":"2019","journal-title":"Soc. Choice Welf."},{"key":"10.1016\/j.mathsocsci.2026.102515_b23","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.mathsocsci.2018.07.001","article-title":"Resource-monotonicity and population-monotonicity in connected cake-cutting","volume":"95","author":"Segal-Halevi","year":"2018","journal-title":"Math. Social Sci."},{"issue":"1","key":"10.1016\/j.mathsocsci.2026.102515_b24","first-page":"101","article-title":"The problem of fair division","volume":"16","author":"Steinhaus","year":"1948","journal-title":"Econometrica"},{"key":"10.1016\/j.mathsocsci.2026.102515_b25","doi-asserted-by":"crossref","unstructured":"Stromquist, W., Envy-free cake divisions cannot be found by finite protocols. Electr. J. Comb. 15 (1), 2008.","DOI":"10.37236\/735"}],"container-title":["Mathematical Social Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165489626000223?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165489626000223?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T05:04:52Z","timestamp":1772600692000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0165489626000223"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3]]},"references-count":25,"alternative-id":["S0165489626000223"],"URL":"https:\/\/doi.org\/10.1016\/j.mathsocsci.2026.102515","relation":{},"ISSN":["0165-4896"],"issn-type":[{"value":"0165-4896","type":"print"}],"subject":[],"published":{"date-parts":[[2026,3]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Between proportionnality and envy-freeness: -proportionality","name":"articletitle","label":"Article Title"},{"value":"Mathematical Social Sciences","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.mathsocsci.2026.102515","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"102515"}}