A bounded utility function probably gets you out of all problems along those lines.
Certainly it’s good in the particular case: your expected utility (in the appropriate sense) is an increasing function of bets you accept and increasing sequences don’t have convergence issues.
How would you bound your utility function? Just pick some arbitrary converging function f, and set utility’ = f(utility)? That seems arbitrary. I suspect it might also make theorems about expectation maximization break down.
No, I’m not advocating changing utility functions. I’m just saying that if your utility function is bounded, you don’t have either of these problems with infinity. You don’t have the convergence problem nor the original problem of probability of the good outcome going to zero. Of course, you still have the result that you keep making bets till your utility is maxed out with very low probability, which bothers some people.
A bounded utility function probably gets you out of all problems along those lines.
Certainly it’s good in the particular case: your expected utility (in the appropriate sense) is an increasing function of bets you accept and increasing sequences don’t have convergence issues.
How would you bound your utility function? Just pick some arbitrary converging function f, and set utility’ = f(utility)? That seems arbitrary. I suspect it might also make theorems about expectation maximization break down.
No, I’m not advocating changing utility functions. I’m just saying that if your utility function is bounded, you don’t have either of these problems with infinity. You don’t have the convergence problem nor the original problem of probability of the good outcome going to zero. Of course, you still have the result that you keep making bets till your utility is maxed out with very low probability, which bothers some people.