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We examine the following question: If a claims problem can be decomposed into smaller claims problems, can the solutions of these smaller problems be added to obtain the solution of the original problem? A natural condition for this decomposition is that the solution to each of the smaller problems is non-degenerate, assigning positive awards to each claimant. We identify the only consistent and endowment monotonic adjudication rules satisfying this property; they are generalizations of the canonical \u201cconstrained equal losses rule\u201d sorting claimants into priority classes and distributing the amount available to each class using a weighted constrained equal losses rule. The constrained equal losses rule is the only symmetric rule in this family of rules.<\/jats:p>","DOI":"10.1007\/s00182-022-00811-6","type":"journal-article","created":{"date-parts":[[2022,11,29]],"date-time":"2022-11-29T15:02:49Z","timestamp":1669734169000},"page":"93-116","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Additive adjudication of conflicting claims"],"prefix":"10.1007","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3112-9275","authenticated-orcid":false,"given":"Jaume","family":"Garc\u00eda-Segarra","sequence":"first","affiliation":[]},{"given":"Miguel","family":"Gin\u00e9s-Vilar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,11,29]]},"reference":[{"issue":"1","key":"811_CR1","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s11750-012-0262-8","volume":"22","author":"J Alcalde","year":"2014","unstructured":"Alcalde J, del Carmen Marco-Gil M, Silva-Reus JA (2014) The minimal overlap rule: restrictions on mergers for creditors\u2019 consensus. 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