You have evidence E and possible explanations A and B. A implies payoff 1 soon, and B implies payoff 0.
When you have utility calculation, estimated p(A) gets multiplied by value of A, estimated p(B) gets multiplied by value of B and you care about difference between to estimations.
Why difference? Well, you should be very happy that you are a human with cognitive capabilities and not a vivisected frog. Or you could be very unhappy that you are not guaranteed to be immortal. Adding either of these large constants to evaluations of all outcomes doesn’t change the difference of two possible situations here and now.
So you calculate p(A)v(A)+p(B)v(B), and if you take a bit of p(A) and give it to p(B) you get Δp(A)(v(A)-v(B)) change.
If you talk about credence, it is another story. You can relatively easily calculate p(E|A) and p(E|B). It is hard to find out p(A) and p(B). Bayesian approach hints that maybe you should just try to find a lot of independent evidence pieces so that their voice can drown the prior difference. But how is evidence summarized? You want to find (prior(A)*p(E|A))/(p(E|A)+p(E|B)) = prior(A)/(1+p(E|B)/p(E|A)). There is ratio of p(E|A) and p(E|B), so you need to look at Δ(p(E|A)/p(E|B)), and this depends on absolute values of probabilities in addition to change.
It is measuring different things.
You have evidence E and possible explanations A and B. A implies payoff 1 soon, and B implies payoff 0.
When you have utility calculation, estimated p(A) gets multiplied by value of A, estimated p(B) gets multiplied by value of B and you care about difference between to estimations.
Why difference? Well, you should be very happy that you are a human with cognitive capabilities and not a vivisected frog. Or you could be very unhappy that you are not guaranteed to be immortal. Adding either of these large constants to evaluations of all outcomes doesn’t change the difference of two possible situations here and now.
So you calculate p(A)v(A)+p(B)v(B), and if you take a bit of p(A) and give it to p(B) you get Δp(A)(v(A)-v(B)) change.
If you talk about credence, it is another story. You can relatively easily calculate p(E|A) and p(E|B). It is hard to find out p(A) and p(B). Bayesian approach hints that maybe you should just try to find a lot of independent evidence pieces so that their voice can drown the prior difference. But how is evidence summarized? You want to find (prior(A)*p(E|A))/(p(E|A)+p(E|B)) = prior(A)/(1+p(E|B)/p(E|A)). There is ratio of p(E|A) and p(E|B), so you need to look at Δ(p(E|A)/p(E|B)), and this depends on absolute values of probabilities in addition to change.
Thanks!
I wonder if it would be worth having a Less Wrong Q&A site, or if that purpose is better served by existing Q&A sites.