Subjective Probability and Lower and Upper Prevision: A New Understanding.

Abstract

This article introduces a new way of understanding subjective probability and its generalization to lower and upper prevision. Instead of asking whether a person is willing to pay given prices for given risky payoffs, we ask whether the person believes he can make a lot of money at those prices. If not—if the person is convinced that no strategy for exploiting the prices can make him very rich in the long run—then the prices measure his subjective uncertainty about the events involved. This new understanding justifies Peter Walley’s updating principle, which applies when new information is anticipated exactly. It also justifies a weaker principle that is more useful for planning because it applies even when new information is not anticipated exactly. This weaker principle can serve as a basis for flexible probabilistic planning in event trees.

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