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CarlShulman comments on Open Thread June 2010, Part 2 - Less Wrong
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This isn't right. The way utility is normally defined, if outcome X has 10 times the utility of outcome Y for a given utility function, agents behaving in accord with that function will be indifferent between certain Y and a 10% probability of X. That's why they call expected utility theory a theory of "decision under uncertainty." The scenario you describe sounds like one where the payoffs are in some currency such that you have declining utility with increasing amounts of the currency.
Uh, no. Allright, lets say I give you a 1 out of 10 chance at winning 10 times everything you own, but the other 9 times you lose everything. The net utility for accepting is the same as not accepting, yet thats completely ignoring the fact that if you do enter, 90 % of the time you lose everything, no matter how high the reward is.
As Thom indicates, this is exactly what I was talking about: ten times the stuff you own, rather than ten times the utility. Since utility is just a representation of your preferences, the 1 in 10 payoff would only have ten times the utility of your current endowment if you would be willing to accept this gamble.
That's only true if "everything you own" is cast in terms of utility, which is not intuitive. Normally, "everything you own" would be in terms of dollars or something to that effect, and ten times the number of dollars I have is not worth 10 times the utility of those dollars.