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Comput."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>\n                    Allocating indivisible goods is a ubiquitous task in fair division. We study\n                    <jats:italic toggle=\"yes\">additive welfarist rules<\/jats:italic>\n                    , an important class of rules which choose an allocation that maximizes the sum of some function of the agents\u2019 utilities. Prior work has shown that the maximum Nash welfare (MNW) rule is the unique additive welfarist rule that guarantees envy-freeness up to one good (EF1). We strengthen this result by showing that MNW remains the only additive welfarist rule that ensures EF1 for identical-good instances, two-value instances, as well as normalized instances with three or more agents. On the other hand, if the agents\u2019 utilities are integers, we demonstrate that several other rules offer the EF1 guarantee, and provide characterizations of these rules for various classes of instances.\n                  <\/jats:p>","DOI":"10.1145\/3793253","type":"journal-article","created":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T11:52:12Z","timestamp":1771501932000},"page":"1-50","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Fairness of Additive Welfarist Rules"],"prefix":"10.1145","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7078-5582","authenticated-orcid":false,"given":"Karen Frilya","family":"Celine","sequence":"first","affiliation":[{"name":"National University of Singapore","place":["Singapore, Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8973-2539","authenticated-orcid":false,"given":"Warut","family":"Suksompong","sequence":"additional","affiliation":[{"name":"National University of Singapore","place":["Singapore, Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8621-5402","authenticated-orcid":false,"given":"Sheung Man","family":"Yuen","sequence":"additional","affiliation":[{"name":"National University of Singapore","place":["Singapore, Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,6,17]]},"reference":[{"key":"e_1_3_4_2_1","first-page":"4760","volume-title":"Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI)","author":"Akrami Hannaneh","year":"2022","unstructured":"Hannaneh Akrami, Bhaskar Ray Chaudhury, Martin Hoefer, Kurt Mehlhorn, Marco Schmalhofer, Golnoosh Shahkarami, Giovanna Varricchio, Quentin Vermande, and Ernest van Wijland. 2022. Maximizing Nash social welfare in 2-value instances. In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI). 4760\u20134767."},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2021.02.020"},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-021-10039-8"},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511598975"},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1086\/664613"},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-011-9359-y"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355902"},{"key":"e_1_3_4_9_1","first-page":"23","volume-title":"Proceedings of the 20th Pacific Rim International Conference on Artificial Intelligence (PRICAI)","author":"Celine Karen Frilya","year":"2023","unstructured":"Karen Frilya Celine, Muhammad Ayaz Dzulfikar, and Ivan Adrian Koswara. 2023. Egalitarian price of fairness for indivisible goods. In Proceedings of the 20th Pacific Rim International Conference on Artificial Intelligence (PRICAI). 23\u201328."},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1053682"},{"key":"e_1_3_4_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/3670865.3673445"},{"issue":"1734","key":"e_1_3_4_12_1","first-page":"150","article-title":"De progressionibus harmonicis observationes","volume":"7","author":"Euler Leonhard","year":"1740","unstructured":"Leonhard Euler. 1740. De progressionibus harmonicis observationes. Commentarii academiae scientiarum Petropolitanae 7, 1734\u201335 (1740), 150\u2013156.","journal-title":"Commentarii academiae scientiarum Petropolitanae"},{"issue":"1","key":"e_1_3_4_13_1","first-page":"45","article-title":"Resource allocation and the public sector","volume":"7","author":"Foley Duncan K.","year":"1967","unstructured":"Duncan K. Foley. 1967. Resource allocation and the public sector. Yale Economics Essays 7, 1 (1967), 45\u201398.","journal-title":"Yale Economics Essays"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2728732.2728738"},{"key":"e_1_3_4_15_1","article-title":"Analytic continuation of harmonic series","author":"Hintze Wolfgang","year":"2019","unstructured":"Wolfgang Hintze. 2019. Analytic continuation of harmonic series. Mathematics Stack Exchange. Retrieved September 30, 2024 from https:\/\/math.stackexchange.com\/q\/3058569","journal-title":"Mathematics Stack Exchange"},{"key":"e_1_3_4_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2017.01.012"},{"key":"e_1_3_4_17_1","doi-asserted-by":"publisher","DOI":"10.5555\/3635637.3662975"},{"key":"e_1_3_4_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/988772.988792"},{"key":"e_1_3_4_19_1","volume-title":"Adnotationes ad calculum integralem Euleri","author":"Mascheroni Lorenzo","year":"1790","unstructured":"Lorenzo Mascheroni. 1790. 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