Savage's Theorem Under Changing Awareness

Franz Dietrich

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Abstract: This paper proposes a simple unified framework of choice under changing awareness, addressing both outcome awareness and (nature) state awareness, and both how fine and how exhaustive the awareness is. Six axioms characterize an (essentially unique) expected-utility rationalization of preferences, in which utilities and probabilities are revised according to three revision rules when awareness changes: (R1) utilities of unaffected outcomes are transformed affinely; (R2) probabilities of unaffected events are transformed proportionally; (R3) enough probabilities ‘objectively' never change (they represent revealed objective risk). Savage's Theorem is a special case of the theorem, namely the special case of fixed awareness, in which our axioms reduce to Savage's axioms while R1 and R2 hold trivially and R3 reduces to Savage's requirement of atomless probabilities. Rule R2 parallels Karni and Viero's (2013) ‘reverse Bayesianism' and Ahn and Ergin's (2010) ‘partition-dependence'. The theorem draws mathematically on Kopylov (2007), Niiniluoto (1972) and Wakker (1981).

Date: 2018-07
New Economics Papers: this item is included in nep-mic and nep-upt
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Published in Journal of Economic Theory, 2018, 176, pp.1-54. ⟨10.1016/j.jet.2018.01.015⟩

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Related works:
Journal Article: Savage's theorem under changing awareness (2018)
Working Paper: Savage's Theorem Under Changing Awareness (2018)
Working Paper: Savage's Theorem Under Changing Awareness (2018)
Working Paper: Savage's Theorem Under Changing Awareness (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-01743898

DOI: 10.1016/j.jet.2018.01.015

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