What if the utility function is bound but and the bound itself is expandable without limit in at least some cases?
For instance, take a hypothetical utility function, Coinflipper bot.
Coinflipper bot has utility equal to the number of fair coins it has flipped.
Coinflipper bot has a utility bound equal to the 2^(greatest number of consecutive heads on fair coins it has flipped+1)
For instance, a particular example of Coinflipper bot might have flipped 512 fair coins and it’s current record is 10 consecutive heads on fair coins, so it’s utility is 512 and it’s utility bound is 2^(10+1) or 2048.
On the other hand, a different instance of Coinflipper bot might have flipped 2 fair coins, gotten 2 tails, and have a utility of 2 and a utility bound of 2^(0+1)=2.
How would the math work out in that kind of situation?
What if, depending on other circumstances(say the flip of a fair coin), your utility function can take values in either a finite(if heads) or infinite(if tails) interval?
Would that entire situation be bounded, unbounded, neither, or is my previous question ill posed?
What if the utility function is bound but and the bound itself is expandable without limit in at least some cases?
For instance, take a hypothetical utility function, Coinflipper bot.
Coinflipper bot has utility equal to the number of fair coins it has flipped.
Coinflipper bot has a utility bound equal to the 2^(greatest number of consecutive heads on fair coins it has flipped+1)
For instance, a particular example of Coinflipper bot might have flipped 512 fair coins and it’s current record is 10 consecutive heads on fair coins, so it’s utility is 512 and it’s utility bound is 2^(10+1) or 2048.
On the other hand, a different instance of Coinflipper bot might have flipped 2 fair coins, gotten 2 tails, and have a utility of 2 and a utility bound of 2^(0+1)=2.
How would the math work out in that kind of situation?
I don’t understand what you mean by “utility bound”. A bounded utility function is just a function which takes values in a finite interval.
Let me try rephrasing this a bit.
What if, depending on other circumstances(say the flip of a fair coin), your utility function can take values in either a finite(if heads) or infinite(if tails) interval?
Would that entire situation be bounded, unbounded, neither, or is my previous question ill posed?