not having to pay D is effectively the same as gaining D
No! If you’re going to add/multiply something to your utility function for convenience, you have to do it for every action. When the building is on fire, deciding whether to turn on the sprinklers is a decision on whether to spend T and gain D, so V(TP)-V(FN) needs to be D-T.
Oh you’re right! Thanks for catching that. I think I was lead astray because I wanted there to be a big payoff for averting the bad event, but I guess the benefit is just not having to pay D. I’ll have a look and see how much this changes things
Edit: Fixed it up now, none of the conclusions seem to change (which is good because they seemed like common sense!). Thanks for reading this and pointing that out!
No! If you’re going to add/multiply something to your utility function for convenience, you have to do it for every action. When the building is on fire, deciding whether to turn on the sprinklers is a decision on whether to spend T and gain D, so V(TP)-V(FN) needs to be D-T.
Oh you’re right! Thanks for catching that. I think I was lead astray because I wanted there to be a big payoff for averting the bad event, but I guess the benefit is just not having to pay D.
I’ll have a look and see how much this changes things
Edit: Fixed it up now, none of the conclusions seem to change (which is good because they seemed like common sense!). Thanks for reading this and pointing that out!