Journal of Risk and Uncertainty

, Volume 10, Issue 1, pp 71–91 | Cite as

Coherent decision analysis with inseparable probabilities and utilities

  • Robert F. Nau


This article explores the extent to which a decision maker's probabilities can be measured separately from his/her utilities by observing his/her acceptance of small monetary gambles. Only a partial separation is achieved: the acceptable gambles are partitioned into a set of “belief gambles,” which reveals probabilities distorted by marginal utilities for money, and a set of “preference gambles,” which reveals utilities reciprocally distorted by marginal utilities for money. However, the information in these gambles still enables us to solve the decision maker's problem: his/her utility-maximizing decision is the one that avoids arbitrage (i.e., incoherence or Dutch books).

Key words

coherence subjective probability state-dependent utility small worlds risk neutral probabilities noncooperative games arbitrage Dutch books 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Robert F. Nau
    • 1
  1. 1.The Fuqua School of BusinessDuke UniversityDurham

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