Coherent choice functions without Archimedeanity

In Thomas Augustin, Fabio Gagliardi Cozman & Gregory Wheeler (eds.), Reflections on the Foundations of Probability and Statistics. Springer Cham (forthcoming)
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Abstract

We study whether it is possible to generalise Seidenfeld et al.’s representation result for coherent choice functions in terms of sets of probability/utility pairs when we let go of Archimedeanity. We show that the convexity property is necessary but not sufficient for a choice function to be an infimum of a class of lexicographic ones. For the special case of two-dimensional option spaces, we determine the necessary and sufficient conditions by weakening the Archimedean axiom.

Author's Profile

Arthur Van Camp
University of Bristol

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