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pengvado comments on Money pumping: the axiomatic approach - Less Wrong
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Thanks, I was wondering if all of the axioms were crucial, or mostly the transitivity one.
Perhaps "incomparable" is the wrong approximation. Perhaps a better way to view it is that I view transactions as having frictional costs (if nothing else, the cost of working out to sufficient precision what my actual preferences are). There are a lot of (A, B) pairs such that, if I had A and was offered B in exchange, I would turn down the offer, and the same if I had B and was offered A.. Very roughly, assume that I treat each exchange transaction as having some probability of going wrong in some way (e.g. failing in such a way that I wind up with neither object), so the new object's utility has to be say 10% higher than the old object's utility to offset the transaction risk.
Would this model leave me vulnerable to being money pumped?
Your model is safe from being money pumped by another agent. The disadvantage is that you'll pass up some certain gains, which is equivalent (modulo loss aversion) to taking on some certain losses. But if you really do think that there is a nonnegligible probability that any given exchange will go bad, then you don't have to violate any of the preference axioms, all your caution is in the probability estimate.