Reflections on the Foundations of Probability and Statistics. Essays in Honor of Teddy Seidenfeld, Springer (Theory and Decision Library A), Cham, pp. 283 – 317, Jan 2023.
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.