Ambiguity, inductive systems, and the modeling of subjective probability judgements

Abstract

Abstract Gambles which induce the decision‐maker to experience ambiguity about the relative likelihood of events often give rise to ambiguity‐seeking and ambiguity‐avoidance, which imply violation of additivity and Savage's axioms. The inability of the subjective Bayesian theory to account for these empirical regularities has determined a dichotomy between normative and descriptive views of subjective probability. This paper proposes a framework within which the two perspectives can be reconciled. First, a formal definition of ambiguity is given over a continuum ranging from ignorance to risk, and including ambiguous contexts as subsets. Second, it is shown that the systems of inductive logic account for the effects of ambiguity. Then, Carnap's X‐system is applied as a psychological model and compared to Einhorn and Hogarth's non‐normative psychological model. Finally, the implications of this research to the modeling of subjective probability judgements are discussed.