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In this paper we present a theory of decomposition in the context of non-additive Expected Utility, such as Anticipated Utility, or Choquet Expected Utility. We show that many of the results used in conventional Expected Utility carry over to these more general frameworks.
If preferences over lotteries depend only on the marginal probability
distributions then in Expected Utility the utility function is additively
decomposable. We show that in Anticipated Utility the marginality condition
not only implies that the utility function is additively decomposable but
also that the distortion function is the identity function. We further
demonstrate that a decision maker who is bivariate risk-neutral has a utility
function that is additively decomposable and a distortion function q
for which
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