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Two common situations give rise to non-Archimedean preferences: random quantities whose values must be greater than every real number, and strict preferences between random quantities that are deemed closer in value than every positive real number. We also show how to extend a non-Archimedean preference to a larger set of random quantities. The random quantities that we consider include real-valued random variables, horse lotteries, and acts in the theory of Savage. In addition, we weaken the state-independent utility assumptions made by the existing theories and give conditions under which the utility that represents preference is the expected value of a state-dependent utility with respect to a probability over states.<\/jats:p>","DOI":"10.1017\/s1755020324000017","type":"journal-article","created":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T09:41:06Z","timestamp":1715679666000},"page":"99-141","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["WHEN NO PRICE IS RIGHT"],"prefix":"10.1017","volume":"18","author":[{"given":"MARK J.","family":"SCHERVISH","sequence":"first","affiliation":[]},{"given":"TEDDY","family":"SEIDENFELD","sequence":"additional","affiliation":[]},{"given":"JOSEPH B.","family":"KADANE","sequence":"additional","affiliation":[]},{"given":"RUOBIN","family":"GONG","sequence":"additional","affiliation":[]},{"given":"RAFAEL B.","family":"STERN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,5,14]]},"reference":[{"key":"S1755020324000017_r10","first-page":"315","article-title":"Reverse Bayesianism: A comment","volume":"10","author":"Chambers","year":"2018","journal-title":"American Economic Journal: Microeconomics"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r1","DOI":"10.1214\/aoms\/1177704255"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r14","DOI":"10.1016\/S0022-0531(03)00166-2"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r36","DOI":"10.1080\/01621459.1990.10474948"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r17","DOI":"10.1016\/j.ecolecon.2004.01.021"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r30","DOI":"10.1007\/s11225-013-9539-7"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r16","DOI":"10.1007\/978-94-017-3329-8"},{"key":"S1755020324000017_r42","first-page":"199","volume-title":"The Open Handbook of Formal Epistemology","author":"Wenmackers","year":"2019"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r27","DOI":"10.1515\/9781400882144"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r33","DOI":"10.1016\/j.jmateco.2015.06.012"},{"key":"S1755020324000017_r12","first-page":"159","volume-title":"Decision Processes","author":"Debreu","year":"1954"},{"key":"S1755020324000017_r21","first-page":"167","volume-title":"Decision Processes","author":"Hausner","year":"1954"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r38","DOI":"10.1016\/j.jmateco.2008.12.002"},{"volume-title":"The Foundations of Statistics","year":"1954","author":"Savage","key":"S1755020324000017_r35"},{"key":"S1755020324000017_r9","first-page":"256","article-title":"Internality, transfer, and infinitesimal modeling of infinite processes","volume":"29","author":"Bottazzi","year":"2020","journal-title":"Philosophia Mathematica"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r26","DOI":"10.1086\/288600"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r23","DOI":"10.1007\/s11229-020-02611-5"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r34","DOI":"10.1515\/9781400884223"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r40","DOI":"10.1007\/BF01766393"},{"volume-title":"Theory of Probability","year":"1974","author":"de Finetti","key":"S1755020324000017_r11"},{"volume-title":"Theory of Games and Economic Behavior","year":"1947","author":"Von Neumann","key":"S1755020324000017_r41"},{"doi-asserted-by":"publisher","key":"S1755020324000017_r2","DOI":"10.2307\/1909888"},{"unstructured":"[29] Pedersen, A. 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