I didn’t mean to imply nonlinear functions are bad. It’s just how humans are.
Picking gambles 1A and 2B, on the other hand, cannot be described by any utility function.
Prospect Theory describes this and even has a post here on lesswrong. My understanding is that humans have both a non-linear utility function as well as a non-linear risk function. This seems like a useful safeguard against imperfect risk estimation.
[Insurance is] not a Dutch Book in the usual sense: it doesn’t guarantee either side a profit.
If you setup your books correctly, then it is guaranteed. A dutch book doesn’t need to work with only one participant, and in fact many dutch books only work with on populations rather than individuals, in the same way insurance only guarantees a profit when properly spread across groups.
Insurance makes a profit in expectation, but an insurance salesman does have some tiny chance of bankruptcy, though I agree that this is not important. What is important, however, is that an insurance buyer is not guaranteed a loss, which is what distinguishes it from other Dutch books for me.
Prospect theory and similar ideas are close to an explanation of why the Allais Paradox occurs. (That is, why humans pick gambles 1A and 2B, even though this is inconsistent.) But, to my knowledge, while utility theory is both a (bad) model of humans and a guide to how decisions should be made, prospect theory is a better model of humans but often describes errors in reasoning.
(That is, I’m sure it prevents people from doing really stupid things in some cases. But for small bets, it’s probably a bad idea; Kahneman suggests teaching yourself out of it by making yourself think ahead to how many such bets you’ll make over a lifetime. This is a frame of mind in which the risk thing is less of a factor.)
I didn’t mean to imply nonlinear functions are bad. It’s just how humans are.
Prospect Theory describes this and even has a post here on lesswrong. My understanding is that humans have both a non-linear utility function as well as a non-linear risk function. This seems like a useful safeguard against imperfect risk estimation.
If you setup your books correctly, then it is guaranteed. A dutch book doesn’t need to work with only one participant, and in fact many dutch books only work with on populations rather than individuals, in the same way insurance only guarantees a profit when properly spread across groups.
Insurance makes a profit in expectation, but an insurance salesman does have some tiny chance of bankruptcy, though I agree that this is not important. What is important, however, is that an insurance buyer is not guaranteed a loss, which is what distinguishes it from other Dutch books for me.
Prospect theory and similar ideas are close to an explanation of why the Allais Paradox occurs. (That is, why humans pick gambles 1A and 2B, even though this is inconsistent.) But, to my knowledge, while utility theory is both a (bad) model of humans and a guide to how decisions should be made, prospect theory is a better model of humans but often describes errors in reasoning.
(That is, I’m sure it prevents people from doing really stupid things in some cases. But for small bets, it’s probably a bad idea; Kahneman suggests teaching yourself out of it by making yourself think ahead to how many such bets you’ll make over a lifetime. This is a frame of mind in which the risk thing is less of a factor.)