Exploitable Preference Changes

There is an extensive literature on the price that one can end up paying if one's choices do not satisfy certain axioms, e.g., Independence of Irrelevant Alternatives (IIA), and Independence (IND). The argument is that one can be turned into a “money pump, ” by another person, in which one will be repeatedly offered a sequence of choices for some small amount of money, but while one will prefer to accept the offer, it will yield no gain whatsoever. That is, on each round one will pay out a small amount of money and receive nothing in return. It is customary to suppose that this provides one with a solid and thoroughly pragmatic argument for retaining the axioms in question. Being turned into a money pump, however, presupposes that in the context of the offers that will be made, one reasons in accordance with backward induction. I argue that in the context of such offers the appeal to backward induction is simply unconvincing. That is, there is no reason to suppose that the conclusions of backward induction in such cases are at all relevant. This, in turn, implies that the dropping of either of the axioms in question does not really pose any pragmatic problem for a rational decision-maker. I close by reflecting on whether there are perhaps other cases in which backward induction is questionable.