Theory and Decision

, Volume 23, Issue 1, pp 25–36 | Cite as

Second-order probabilities and belief functions

  • Jonathan Baron


A second-order probability Q(P) may be understood as the probability that the true probability of something has the value P. “True” may be interpreted as the value that would be assigned if certain information were available, including information from reflection, calculation, other people, or ordinary evidence. A rule for combining evidence from two independent sources may be derived, if each source i provides a function Q i (P). Belief functions of the sort proposed by Shafer (1976) also provide a formula for combining independent evidence, Dempster's rule, and a way of representing ignorance of the sort that makes us unsure about the value of P. Dempster's rule is shown to be at best a special case of the rule derived in connection with second-order probabilities. Belief functions thus represent a restriction of a full Bayesian analysis.


Bayesian Analysis Independent Source Belief Function True Probability Independent Evidence 
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Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • Jonathan Baron
    • 1
  1. 1.Psychology DepartmentUniversity of PennsylvaniaPhiladelphiaU.S.A.

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