Theory and Decision

, Volume 37, Issue 3, pp 267–309 | Cite as

A challenge to the compound lottery axiom: A two-stage normative structure and comparison to other theories

  • Donald B. Davis
  • M.-Elisabeth Paté-Cornell
Article

Abstract

This paper examines preferences among uncertain prospects when the decision maker is uneasy about his assignment of subjective probabilities. It proposes a two-stage lottery framework for the analysis of such prospects, where the first stage represents an assessment of the vagueness (ambiguity) in defining the problem's randomness and the second stage represents an assessment of the problem for each hypothesized randomness condition. Standard axioms of rationality are prescribed for each stage, including weak ordering, continuity, and strong independence. The ‘Reduction of Compound Lotteries' axiom is weakened, however, so that the two lottery stages have consistent, but not collapsible, preference structures. The paper derives a representation theorem from the primitive preference axioms, and the theorem asserts that preference-consistent decisions are made as if the decision maker is maximizing a modified expected utility functional. This representation and its implications are compared to alternative decision models. Criteria for assigning the relative empirical power of the alternative models are suggested.

Keywords

Ambiguity rationality decision compound lottery two-stage lottery 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Donald B. Davis
    • 1
  • M.-Elisabeth Paté-Cornell
    • 2
  1. 1.Lockheed Missiles and Space Co.SunnyvaleUSA
  2. 2.Department of Industrial Engineering and Engineering ManagementStanford UniversityStanfordUSA

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