It looks to me like the “updatelessness trick” you describe (essentially, behaving as though certain non-local branches of the decision tree are still counterfactually relevant even though they are not — although note that I currently don’t see an obvious way to use that to avoid the usual money pump against intransitivity) recovers most of the behavior we’d see under VNM anyway; and so I don’t think I understand your confusion re: VNM axioms.
E.g. can you give me a case in which (a) we have an agent that exhibits preferences against whose naive implementation there exists some kind of money pump (not necessarily a repeatable one), (b) the agent can implement the updatelessness trick in order to avoid the money pump without modifying their preferences, and yet (c) the agent is not then representable as having modified their preferences in the relevant way?
What I meant by updatelessness removes most of the justification is the reason given here at the very beginning of “Against Resolute Choice”. In order to make a money pump that leads the agent in a circle, the agent has to continue accepting trades around a full preference loop. But if it has decided on the entire plan beforehand, it will just do any plan that involves <1 trip around the preference loop. (Although it’s unclear how it would settle on such a plan, maybe just stopping its search after a given time). It won’t (I think?) choose any plan that does multiple loops, because they are strictly worse.
After choosing this plan though, I think it is representable as VNM rational, as you say. And I’m not sure what to do with this. It does seem important.
However, I think Scott’s argument here satisfies (a) (b) and (c). I think the independence axiom might be special in this respect, because the money pump for independence is exploiting an update on new information.
I don’t think agents that avoid the money pump for cyclicity are representable as satisfying VNM, at least holding fixed the objects of preference (as we should). Resolute choosers with cyclic preferences will reliably choose B over A- at node 3, but they’ll reliably choose A- over B if choosing between these options ex nihilo. That’s not VNM representable, because it requires that the utility of A- be greater than the utility of B and. that the utility of B be greater than the utility of A-
It looks to me like the “updatelessness trick” you describe (essentially, behaving as though certain non-local branches of the decision tree are still counterfactually relevant even though they are not — although note that I currently don’t see an obvious way to use that to avoid the usual money pump against intransitivity) recovers most of the behavior we’d see under VNM anyway; and so I don’t think I understand your confusion re: VNM axioms.
E.g. can you give me a case in which (a) we have an agent that exhibits preferences against whose naive implementation there exists some kind of money pump (not necessarily a repeatable one), (b) the agent can implement the updatelessness trick in order to avoid the money pump without modifying their preferences, and yet (c) the agent is not then representable as having modified their preferences in the relevant way?
Good point.
What I meant by updatelessness removes most of the justification is the reason given here at the very beginning of “Against Resolute Choice”. In order to make a money pump that leads the agent in a circle, the agent has to continue accepting trades around a full preference loop. But if it has decided on the entire plan beforehand, it will just do any plan that involves <1 trip around the preference loop. (Although it’s unclear how it would settle on such a plan, maybe just stopping its search after a given time). It won’t (I think?) choose any plan that does multiple loops, because they are strictly worse.
After choosing this plan though, I think it is representable as VNM rational, as you say. And I’m not sure what to do with this. It does seem important.
However, I think Scott’s argument here satisfies (a) (b) and (c). I think the independence axiom might be special in this respect, because the money pump for independence is exploiting an update on new information.
I don’t think agents that avoid the money pump for cyclicity are representable as satisfying VNM, at least holding fixed the objects of preference (as we should). Resolute choosers with cyclic preferences will reliably choose B over A- at node 3, but they’ll reliably choose A- over B if choosing between these options ex nihilo. That’s not VNM representable, because it requires that the utility of A- be greater than the utility of B and. that the utility of B be greater than the utility of A-