Sorry, I might be just blinded by the technical language, but I’m not seeing why that link invalidates my comment. Could you maybe pull a quote, or even clarify?
Such as, for example, the fact that killing 3^^^^^^3 people shouldn’t be OK because there’s still 3^^^3 people left and my happiness meter is maxed out anyway.
E.g. the example above suggests something like a utility function of the form “utility equals the amount of quantity A for A<S, otherwise utility is equal to S” which rejects free-lunch increases in happy-years. But it’s easy to formulate a bounded utility function that takes such improvements, without being fanatical in the tradeoffs made.
Trivially, it’s easy to give a bounded utility function that always prefers a higher finite quantity of A but still converges, although eventually the preferences involved have to become very weak cardinally. A function with such a term on human happiness would not reject an otherwise “free lunch”. You never “max out,” just become willing to take smaller risks for incremental gains.
Less trivially, one can include terms like those in the bullet-pointed lists at the linked discussion, mapping to features that human brains distinguish and care about enough to make tempting counterexamples: “but if we don’t account for X, then you wouldn’t exert modest effort to get X!” Terms for relative achievement, e.g. the proportion (or adjusted proportion) of potential good (under some scheme of counterfactuals) achieved, neutralize an especially wide range of purported counterexamples.
E.g. the example above suggests something like a utility function of the form “utility equals the amount of quantity A for A<S, otherwise utility is equal to S” which rejects free-lunch increases in happy-years. But it’s easy to formulate a bounded utility function that takes such improvements, without being fanatical in the tradeoffs made.
… it is? Maybe I’m misusing the term “bounded utility function”. Could you elaborate on this?
Yes, I think you are misusing the term. It’s the utility that’s bounded, not the inputs. Say that U=1-(1/(X^2) and 0 when X=0, and X is the quantity of some good. Then utility is bounded between 0 and 1, but increasing X from 3^^^3 to 3^^^3+1 or 4^^^^4 will still (exceedingly slightly) increase utility. It just won’t take risks for small increases in utility. However, terms in the bounded utility function can give weight to large numbers, to relative achievement, to effort, and all the other things mentioned in the discussion I linked, so that one takes risks for those.
Bounded utility functions still seem to cause problems when uncertainty is involved. For example, consider the aforementioned utility function U(n) = 1 - (1 / (n^2)), and let n equal the number of agents living good lives. Using this function, the utility of a 1 in 1 chance of there being 10 agents living good lives equals 1 - (1 / (10^2)) = 0.99, and the utility of a 9 in 10 chance of 3^^^3 agents living good lives and a 1 in 10 chance of no agents living good lives roughly equals 0.1 0 + 0.9 1 = 0.9. Thus, in this situation the agent would be willing to kill (3^^^3) − 10 agents in order to prevent a 0.1 chance of everyone dying, which doesn’t seem right at all. You could modify the utility function, but I think this issue would still to exist to some extent.
Bounded utility functions can represent more than your comment suggests, depending on what terms are included. See this discussion.
Sorry, I might be just blinded by the technical language, but I’m not seeing why that link invalidates my comment. Could you maybe pull a quote, or even clarify?
E.g. the example above suggests something like a utility function of the form “utility equals the amount of quantity A for A<S, otherwise utility is equal to S” which rejects free-lunch increases in happy-years. But it’s easy to formulate a bounded utility function that takes such improvements, without being fanatical in the tradeoffs made.
Trivially, it’s easy to give a bounded utility function that always prefers a higher finite quantity of A but still converges, although eventually the preferences involved have to become very weak cardinally. A function with such a term on human happiness would not reject an otherwise “free lunch”. You never “max out,” just become willing to take smaller risks for incremental gains.
Less trivially, one can include terms like those in the bullet-pointed lists at the linked discussion, mapping to features that human brains distinguish and care about enough to make tempting counterexamples: “but if we don’t account for X, then you wouldn’t exert modest effort to get X!” Terms for relative achievement, e.g. the proportion (or adjusted proportion) of potential good (under some scheme of counterfactuals) achieved, neutralize an especially wide range of purported counterexamples.
… it is? Maybe I’m misusing the term “bounded utility function”. Could you elaborate on this?
Yes, I think you are misusing the term. It’s the utility that’s bounded, not the inputs. Say that U=1-(1/(X^2) and 0 when X=0, and X is the quantity of some good. Then utility is bounded between 0 and 1, but increasing X from 3^^^3 to 3^^^3+1 or 4^^^^4 will still (exceedingly slightly) increase utility. It just won’t take risks for small increases in utility. However, terms in the bounded utility function can give weight to large numbers, to relative achievement, to effort, and all the other things mentioned in the discussion I linked, so that one takes risks for those.
Bounded utility functions still seem to cause problems when uncertainty is involved. For example, consider the aforementioned utility function U(n) = 1 - (1 / (n^2)), and let n equal the number of agents living good lives. Using this function, the utility of a 1 in 1 chance of there being 10 agents living good lives equals 1 - (1 / (10^2)) = 0.99, and the utility of a 9 in 10 chance of 3^^^3 agents living good lives and a 1 in 10 chance of no agents living good lives roughly equals 0.1 0 + 0.9 1 = 0.9. Thus, in this situation the agent would be willing to kill (3^^^3) − 10 agents in order to prevent a 0.1 chance of everyone dying, which doesn’t seem right at all. You could modify the utility function, but I think this issue would still to exist to some extent.
Ah, OK, I was thinking of a bounded utility function as one with a “cutoff point”, yes. You’re absolutely right.