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

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
Keywords duplex decomposition  functional equation  Shannon entropy  gamble decomposition  inset entropy  segregation  utility of gambling  valued events
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DOI 10.1007/s11238-007-9065-z
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A Mathematical Theory of Communication.Claude E. Shannon - 1948 - Bell System Technical Journal 27:379–423.
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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