Savage's theorem under changing awareness

Franz Dietrich

Journal of Economic Theory, 2018, vol. 176, issue C, 1-54

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).

Keywords: Decision under uncertainty; Outcome unawareness versus state unawareness; Non-fine versus non-exhaustive awareness; Utility revision versus probability revision; Small worlds versus grand worlds (search for similar items in EconPapers)
JEL-codes: D81 D83 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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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 (2018)
Working Paper: Savage's Theorem Under Changing Awareness (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:176:y:2018:i:c:p:1-54

DOI: 10.1016/j.jet.2018.01.015

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