A new understanding of subjective probability and its generalization to lower and upper prevision

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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. © 2002 Elsevier Science Inc. All rights reserved.

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Shafer, G., Gillett, P. R., & Scherl, R. B. (2003). A new understanding of subjective probability and its generalization to lower and upper prevision. International Journal of Approximate Reasoning, 33(1), 1–49. https://doi.org/10.1016/S0888-613X(02)00134-2

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