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Representation of strongly independent preorders by vector-valued functions

McCarthy, David and Mikkola, Kalle and Thomas, Teruji (2017): Representation of strongly independent preorders by vector-valued functions.

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Abstract

We show that without assuming completeness or continuity, a strongly independent preorder on a possibly infinite dimensional convex set can always be given a vector-valued representation that naturally generalizes the standard expected utility representation. More precisely, it can be represented by a mixture-preserving function to a product of lexicographic function spaces.

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