I edited this comment to include the statement that “bounded utility means that if U(Y) is too high, U(X) cannot have a double utility etc.” But then it occurred to me that I should say something else, which I’m adding here because I don’t want to keep changing the comment.
Evand’s statement that “these behaviors are both fairly weird (except in the universe where there’s no possible construction for an outcome with double the utility of Y, or the universe where you can’t construct a sufficiently low probability for some reason)” implies a particular understanding of bounded utility.
For example, someone could say, “My utility is in lives saved, and goes up to 10,000,000,000.” In this way he would say that saving 7 billion lives has a utility of 7 billion, saving 9 billion lives has a utility of 9 billion, and so on. But since he is bounding his utility, he would say that saving 20 billion lives has a utility of 10 billion, and so with saving any other number of lives over 10 billion.
This is definitely weird behavior. But this is not what I am suggesting by bounded utility. Basically I am saying that someone might bound his utility at 10 billion, but keep his order of preferences so that e.g. he would always prefer saving more lives to saving less.
This of course leads to something that could be considered scope insensitivity: a person will prefer a chance of saving 10 billion lives to a chance ten times as small of saving 100 billion lives, rather than being indifferent. But basically according to Kaj’s post this is the behavior we were trying to get to in the first place, namely ignoring the smaller probability bet in certain circumstances. It does correspond to people’s behavior in real life, and it doesn’t have the “switching preferences” effect that Kaj’s method will have when you change probabilities.
I edited this comment to include the statement that “bounded utility means that if U(Y) is too high, U(X) cannot have a double utility etc.” But then it occurred to me that I should say something else, which I’m adding here because I don’t want to keep changing the comment.
Evand’s statement that “these behaviors are both fairly weird (except in the universe where there’s no possible construction for an outcome with double the utility of Y, or the universe where you can’t construct a sufficiently low probability for some reason)” implies a particular understanding of bounded utility.
For example, someone could say, “My utility is in lives saved, and goes up to 10,000,000,000.” In this way he would say that saving 7 billion lives has a utility of 7 billion, saving 9 billion lives has a utility of 9 billion, and so on. But since he is bounding his utility, he would say that saving 20 billion lives has a utility of 10 billion, and so with saving any other number of lives over 10 billion.
This is definitely weird behavior. But this is not what I am suggesting by bounded utility. Basically I am saying that someone might bound his utility at 10 billion, but keep his order of preferences so that e.g. he would always prefer saving more lives to saving less.
This of course leads to something that could be considered scope insensitivity: a person will prefer a chance of saving 10 billion lives to a chance ten times as small of saving 100 billion lives, rather than being indifferent. But basically according to Kaj’s post this is the behavior we were trying to get to in the first place, namely ignoring the smaller probability bet in certain circumstances. It does correspond to people’s behavior in real life, and it doesn’t have the “switching preferences” effect that Kaj’s method will have when you change probabilities.