After having read this over twice and read all the comments, I still find myself confused. Isn’t the bounded mugging simply predicated on a really strange definition of a utility function? The “simplest” bounded utility function I can think of is time-invariant, in the sense that it should output the same utilities, or the same preference ordering over your choices, whether you’re 4^^^^4 years old or merely a billion.
The idea that as you live longer you “accumulate” utility seems to run counter to the basic definition of a utility function (e.g. nyan sandwich’s recent post). This idea can be salvaged by saying that your utility function has a term in it for how long you’ve been alive, and having the bound decrease in proportion to that, but I’m just really not sure why you would want to do that. Without this time term, it seems that you’d simply consider whether gaining ~19 utils * miniscule probability is worth it, and reject the offer in the usual way, since you still have plenty of options for getting ~100.
After having read this over twice and read all the comments, I still find myself confused. Isn’t the bounded mugging simply predicated on a really strange definition of a utility function? The “simplest” bounded utility function I can think of is time-invariant, in the sense that it should output the same utilities, or the same preference ordering over your choices, whether you’re 4^^^^4 years old or merely a billion.
The idea that as you live longer you “accumulate” utility seems to run counter to the basic definition of a utility function (e.g. nyan sandwich’s recent post). This idea can be salvaged by saying that your utility function has a term in it for how long you’ve been alive, and having the bound decrease in proportion to that, but I’m just really not sure why you would want to do that. Without this time term, it seems that you’d simply consider whether gaining ~19 utils * miniscule probability is worth it, and reject the offer in the usual way, since you still have plenty of options for getting ~100.