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Stuart_Armstrong 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?
In a certain sense, it does (as long as your 10% beliefs are inaccurate). If you have a lottery A that gives you negative value, I can trade it for a lottery B that is slightly more negative (you 10% chance of getting neither will make you accept this deal). And then itterate.
Or, what about me selling you (in a single transaction) an insurance, good for a hundred trades, that guarantees you against the 10% loss chance?
Generally, inaccurate beliefs leave you open to some sort of arbitrage, even if it's not technically a money pump as described above.