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We revisit and reinterpret Selten's concept of subgame perfectness in thecontext of single agent normal form sequential decision making, which leads usto the concept of subtree perfectness. Thereby, we extend Hammond'scharacterization of extensive form consequentialist consistent behaviour normsto the normal form and to arbitrary choice functions under very fewassumptions. In particular, we do not need to assume probabilities on any eventor utilities on any reward. We show that subtree perfectness is equivalent tonormal-extensive form equivalence, and is sufficient, but, perhapssurprisingly, not necessary, for backward induction to work.

Subtree perfectness, backward induction, and normal-extensive form  equivalence for single agent sequential decision making under arbitrary  choice functions