It seems correct that if you have a planner operating over the full set of transition you’ll ever see, the it can avoid money-pumping of this kind. However it doesn’t seem to hold that this prevents money-pumping in general.
Consider, you have a preference that at some specific future time you will get C > B > A > C, and this preference is independent of how much cash you have. You have a a voucher that will pay out to A at that time, which you value only instrumentally. You start with no access to any trades.
Someone comes up to you and offers you a voucher for B in exchange for your voucher for A and epsilon cash. Let’s not assume any knowledge of any future trades you might be offered. What decision do you make? If a preference is useful for anything it surely should inform you what decision to make, and if preference is meant for anything it should surely say that the chosen actions result in it. If the result of planning is anything but ‘take the trade’ I don’t know what properties this preference ordering has that would give it that label.
Though, I suppose this argument generalizes. If you believe only C > B > A, you might still take a trade from B to A if you expect it’s sufficiently more probable to let you trade to C. If you have persistently wrong non-static expectations, those might be pumped for money the same way. Another way to put this is maybe that trying to value access to states independently of their trade value doesn’t work.
I’ve no doubt that it’s possible to make a planner that’s somewhat robust to inconsistent preference ordering, but this does seem driven by the fact we’ve not given the term ‘preference ordering’ any coherent meaning yet and have no coherent measure of success. Once you demand those it would be easier to point at any flaws.
It seems correct that if you have a planner operating over the full set of transition you’ll ever see, the it can avoid money-pumping of this kind. However it doesn’t seem to hold that this prevents money-pumping in general.
Consider, you have a preference that at some specific future time you will get C > B > A > C, and this preference is independent of how much cash you have. You have a a voucher that will pay out to A at that time, which you value only instrumentally. You start with no access to any trades.
Someone comes up to you and offers you a voucher for B in exchange for your voucher for A and epsilon cash. Let’s not assume any knowledge of any future trades you might be offered. What decision do you make? If a preference is useful for anything it surely should inform you what decision to make, and if preference is meant for anything it should surely say that the chosen actions result in it. If the result of planning is anything but ‘take the trade’ I don’t know what properties this preference ordering has that would give it that label.
Though, I suppose this argument generalizes. If you believe only C > B > A, you might still take a trade from B to A if you expect it’s sufficiently more probable to let you trade to C. If you have persistently wrong non-static expectations, those might be pumped for money the same way. Another way to put this is maybe that trying to value access to states independently of their trade value doesn’t work.
I’ve no doubt that it’s possible to make a planner that’s somewhat robust to inconsistent preference ordering, but this does seem driven by the fact we’ve not given the term ‘preference ordering’ any coherent meaning yet and have no coherent measure of success. Once you demand those it would be easier to point at any flaws.