The utility function assumes that you play the “game” (situation, whatever) an infinite number of times and then find the net utility. Thats good when your playing the “game” enough times to matter. It’s not when your only playing a small number of times. So lets look at it as “winning” or “loosing”. If the odds are really low and the risk is high and your only playing once, then most of the time you expect to loose. If you do it enough times, you even the odds out and the loss gets canceled out by the large reward, but only playing once you expect to loose more then you gain. Why would you assume differnetly? Thats my 2 cents and so far its the only way I have come up with to navigate around this problem.
The utility function assumes that you play the “game” (situation, whatever) an infinite number of times and then find the net utility.
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.
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.
The utility function assumes that you play the “game” (situation, whatever) an infinite number of times and then find the net utility. Thats good when your playing the “game” enough times to matter. It’s not when your only playing a small number of times. So lets look at it as “winning” or “loosing”. If the odds are really low and the risk is high and your only playing once, then most of the time you expect to loose. If you do it enough times, you even the odds out and the loss gets canceled out by the large reward, but only playing once you expect to loose more then you gain. Why would you assume differnetly? Thats my 2 cents and so far its the only way I have come up with to navigate around this problem.
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.