With a given probability of nuclear war, we don't care about the utility difference between war and not war; we care about the difference between preparations succeed and preparations fail, which is the probability we are trying to control when buying a fallout shelter.

I'm not sure I agree. When optimizing for utility across one's lifespan, it's important to note that years of post-nuke life are both more expensive and carry less utility than years of non-nuke life. So when you evaluate the utility/dollar of building a fallout shelter and compare it to the utility/dollar of other potential investments, you need to put a discount factor on the years of life you expect your shelter to gain for you in the event of a war.

For instance, if I expected with 50% confidence a nuclear war that will certainly kill me if it occurs while I am unprotected and were presented with the following options:

• Option A: Purchase a bomb shelter that will grant ten years of post-nuke life in the event of a nuclear war but will grant no benefit in the event of no nuclear war

• Option B: Purchase an experimental health intervention that will grant on average five years of additional healthy life in the event of no nuclear war, but have no effect in the event of a nuclear war (as I'll die before getting to benefit)

I would probably consider option B to be superior to option A, because my intuitions suggest that the utility of post-nuclear life would be massively discounted.