Estimation of Subjective Probabilities through the Prism of Karni-Jaffray Theorem and Stochastic Approximation

Theoretical formulations deriving from a theorem of Karni-Jaffray under the light of the Savage and von Neumann theory are discussed in the paper. The main purpose is to develop an approximation based methodology for the assessment of subjective probabilities. The basic information is the decision-maker (DM) preferences explicitly expressed in a cardinal way (‘yes’, ‘no’, ‘no preference’). The elicitation procedure uses the Lpτ pseudo-random Sobol’ sequences and the stochastic approximation approach. The dialog DM-computer is modeled numerically and the results are presented.