  This paper studies and bounds the effects of approximating loss functions and
credal sets on choice functions, under very weak assumptions. 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.
