{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T00:45:14Z","timestamp":1711500314032},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T00:00:00Z","timestamp":1673827200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Scoring rules measure the deviation between a forecast, which assigns degrees of confidence to various events, and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast <jats:italic>p<\/jats:italic> by the lights of <jats:italic>p<\/jats:italic> is strictly better than the mathematical expectation of any other forecast <jats:italic>q<\/jats:italic> by the lights of <jats:italic>p<\/jats:italic>. Forecasts need not satisfy the axioms of the probability calculus, but Predd et al. [9] have shown that given a finite sample space and any strictly proper <jats:italic>additive and continuous<\/jats:italic> scoring rule, the score for any forecast that does not satisfy the axioms of probability is strictly dominated by the score for some probabilistically consistent forecast. Recently, this result has been extended to non-additive continuous scoring rules. In this paper, a condition weaker than continuity is given that suffices for the result, and the condition is proved to be optimal.<\/jats:p>","DOI":"10.1017\/s1755020323000035","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T13:49:37Z","timestamp":1673876977000},"page":"132-143","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["NECESSARY AND SUFFICIENT CONDITIONS FOR DOMINATION RESULTS FOR PROPER SCORING RULES"],"prefix":"10.1017","volume":"17","author":[{"given":"ALEXANDER R.","family":"PRUSS","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,1,16]]},"reference":[{"key":"S1755020323000035_r6","doi-asserted-by":"publisher","DOI":"10.1017\/psa.2021.43"},{"key":"S1755020323000035_r2","unstructured":"[2] fedja (2021) Answer to: If a Convex Compact Set Meets the Positive Orthant Does It Meet It at a Point with a Normal in the Positive Orthant? Mathoverflow. Available from: https:\/\/mathoverflow.net\/questions\/384140."},{"key":"S1755020323000035_r7","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198732716.001.0001"},{"key":"S1755020323000035_r4","doi-asserted-by":"publisher","DOI":"10.1093\/mind\/fzl607"},{"key":"S1755020323000035_r3","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000001437"},{"key":"S1755020323000035_r8","doi-asserted-by":"publisher","DOI":"10.1017\/psa.2021.17"},{"key":"S1755020323000035_r9","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2027573"},{"key":"S1755020323000035_r11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02431-3"},{"key":"S1755020323000035_r10","unstructured":"[10] Pruss, A. R. (2021). Proper scoring rules and domination. Preprint, arXiv:2102.02260."},{"key":"S1755020323000035_r1","doi-asserted-by":"publisher","DOI":"10.1007\/s40300-014-0039-y"},{"key":"S1755020323000035_r5","doi-asserted-by":"publisher","DOI":"10.1086\/392661"},{"key":"S1755020323000035_r12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02562681"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020323000035","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T09:48:46Z","timestamp":1711446526000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020323000035\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,16]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["S1755020323000035"],"URL":"https:\/\/doi.org\/10.1017\/s1755020323000035","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,16]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}