Utility of Gambling when Events are Valued: an Application of Inset Entropy [Book Review]

Theory and Decision 67 (1):23-63 (2009)
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Abstract

The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights—a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, this becomes one of several standard utility representations, plus a weighted value function over events, plus an entropy term of the weights. In the finitely additive case, the latter is the Shannon entropy; in all other cases it is entropy of degree not 1. The primary mathematical tool is the theory of inset entropy

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A Mathematical Theory of Communication.Claude Elwood Shannon - 1948 - Bell System Technical Journal 27 (April 1924):379–423.
On Elements of Chance.R. Duncan Luce & Anthony A. J. Marley - 2000 - Theory and Decision 49 (2):97-126.
On Elements of Chance.R. Duncan Luce & A. A. J. Marley - 2000 - Theory and Decision 49 (2):97-126.

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