The Anscombe–Aumann representation and the independence axiom: a reconsideration

Abhinash Borah, Christopher Kops

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We provide a new behavioral foundation for subjective expected utility (SEU) within the Anscombe–Aumann framework. In contrast to the original axiomatization of SEU, our behavioral foundation establishes that to be consistent with SEU maximization, we need not explicitly assume that preferences satisfy the independence axiom over the domain of all acts. Rather, the substantive implications of independence for an SEU representation may equivalently be derived from less demanding conditions over certain smaller classes of acts. These acts, which we refer to as uncertainty-free comparable acts, have the property that they are relatively simple for a decision maker to compare because she can rank acts within any such class based on her risk preferences alone, without having to consider the underlying uncertainty. Acts of this kind comprise constant acts and acts that are almost identical in the sense that they differ from one another in at most one state.
Original languageEnglish
Pages (from-to)211-226
Number of pages16
JournalTheory and Decision
Volume80
DOIs
Publication statusPublished - 2016
Externally publishedYes

Keywords

  • Subjective expected utility
  • Anscombe-Aumann model
  • Independence axiom
  • Uncertainty-free comparable acts

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