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AndrewKemendo comments on Consequences of arbitrage: expected cash - Less Wrong
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Comments (27)
Sticking with expected utility works in theory if you have a discrete number of variables (options) and can discern between all variables such that they can be judged equally and the cost (in time or whatever) is not greater than the marginal gain from the process. Here is an example I like: Go to the supermarket and optimize your expected utility for breakfast cereal.
The money pump only works if your "utility function" is static, or more accurately, if your preferences update slower than the pumper can change the statistical trade imbalance eg: arbitrage doesn't work if the person outsourced to can also outsource.
I can take advantage of your vN-M axioms if I have any information about one of your preferences which you do not have (this need not be gotten illegally), as a result, you sticking to it would money pump regardless.
This sounds like an even better reason to use expected utility! If you have ignorance about your preferences, then you should reduce the amount of other unknowns, and hence simplify your decision theory to expected utility.
"The power's out at my house and I need a game I can play." "I guess you need something that doesn't require electricity. I have just the thing: a pencil!"
Expected utility has one of the traits needed of a decision theory. As AndrewKemendo points out, it does not have all of them.