Why would you expect her to be able to diminish the probability of doom by spending her million dollars? Situations where someone can have a detectable impact on global-scale problems by spending only a million dollars are extraordinarily rare. It seems doubtful that there are even ways to spend a million dollars on decreasing AI xrisk now when timelines are measured in years (as the projects working on it do not seem to be meaningfully funding-constrained), much less if you expected the xrisk to materialize with 50% probability tomorrow (less time than it takes to e.g. get a team of researchers together).
I agree it’s rare to have a global impact with a million dollars. But if you’re 50% confident the world will be destroyed tomorrow, that implies you have some sort of specific knowledge about the mechanism of destruction. The reason it’s hard to spend a million dollars to have a big impact is often because of a lack of such specific information.
But if you are adding the stipulation that there’s nothing Alice can do to affect the probability of doom, then I agree that your math checks out.
Why would you expect her to be able to diminish the probability of doom by spending her million dollars? Situations where someone can have a detectable impact on global-scale problems by spending only a million dollars are extraordinarily rare. It seems doubtful that there are even ways to spend a million dollars on decreasing AI xrisk now when timelines are measured in years (as the projects working on it do not seem to be meaningfully funding-constrained), much less if you expected the xrisk to materialize with 50% probability tomorrow (less time than it takes to e.g. get a team of researchers together).
I agree it’s rare to have a global impact with a million dollars. But if you’re 50% confident the world will be destroyed tomorrow, that implies you have some sort of specific knowledge about the mechanism of destruction. The reason it’s hard to spend a million dollars to have a big impact is often because of a lack of such specific information.
But if you are adding the stipulation that there’s nothing Alice can do to affect the probability of doom, then I agree that your math checks out.