Savage's Theorem Under Changing Awareness

Dietrich, Franz (2016): Savage's Theorem Under Changing Awareness.

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, obtained in the case of fully fixed awareness, as then 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).

• Item Type: MPRA Paper
• Language: English
• 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
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty

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