We prove necessary and sufficient conditions on choice functions for factuality to hold in normal form sequential decision problems. We find that factuality is sufficient for backward induction to work. However, choice must be induced by a total preorder for factuality to hold. Hence, many of the optimality criteria used in imprecise probability theory (such as interval dominance, maximality, and E-admissibility) are counterfactual under normal form decision making.
Keywords. counterfactual, partial ordering, optimality, decision trees, choice functions, backward induction
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