This paper studies and bounds the effects of approximating loss functions and credal sets, under very weak assumptions, on choice functions. In particular, the credal set is assumed to be neither convex nor closed. The main result is that the effects of approximation can be bounded, although in general, approximation of the credal set may not always be practically possible. In case of pairwise choice, I demonstrate how the situation can be improved by showing that only approximations of the extreme points of the closure of the convex hull of the credal set need to be taken into account, as expected.
Keywords. decision making, approximation, E-admissibility, maximality, numerical analysis, lower prevision, sensitivity analysis
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