If you have an unbounded utility function and a broad prior, then expected utility calculations don’t converge. It’s not that decision theory is producing an answer and we are rejecting it—decision theory isn’t saying anything. This paper by Peter de Blanc makes the argument. The unbounded cases is just as bad as the infinite case. Put a different way, the argument for representing preferences by utility functions doesn’t go through in cases where there are infinitely many possible outcomes.
That said, most people report that they wouldn’t make the trade, from which we can conclude that their utility functions are bounded, and so we don’t even have to worry about any of this.
I think that the argument you give—that there are much better ways of securing very large payoffs—is also an important part of making intuitive sense of the picture. The mugger was only ever a metaphor, there is no plausible view on which you’d actually pay. If you are sloppy you might conclude that there is some mugger with expected returns twice as large as whatever other plausible use of the money you are considering, but of course all of this is just an artifact of rearranging divergent sums.
If you have an unbounded utility function and a broad prior, then expected utility calculations don’t converge.
That is the core of what replying to zulu’s post made me think.
I won’t say too much more until I read up on more existent thoughts, but I as of now I strongly object to this
That said, most people report that they wouldn’t make the trade, from which we can conclude that their utility functions are bounded, and so we don’t even have to worry about any of this.
I neither think that the conclusion follows, nor that utility functions should ever be bounded. We need another way to model this.
If you have an unbounded utility function and a broad prior, then expected utility calculations don’t converge. It’s not that decision theory is producing an answer and we are rejecting it—decision theory isn’t saying anything. This paper by Peter de Blanc makes the argument. The unbounded cases is just as bad as the infinite case. Put a different way, the argument for representing preferences by utility functions doesn’t go through in cases where there are infinitely many possible outcomes.
That said, most people report that they wouldn’t make the trade, from which we can conclude that their utility functions are bounded, and so we don’t even have to worry about any of this.
I think that the argument you give—that there are much better ways of securing very large payoffs—is also an important part of making intuitive sense of the picture. The mugger was only ever a metaphor, there is no plausible view on which you’d actually pay. If you are sloppy you might conclude that there is some mugger with expected returns twice as large as whatever other plausible use of the money you are considering, but of course all of this is just an artifact of rearranging divergent sums.
That is the core of what replying to zulu’s post made me think.
I won’t say too much more until I read up on more existent thoughts, but I as of now I strongly object to this
I neither think that the conclusion follows, nor that utility functions should ever be bounded. We need another way to model this.