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