I think there are several things wrong with the Equal Weight View, but I think this is the easiest way to see it:
Let’s say I have O(H)=2:1 which I updated from a prior of 1:6. Now I meet someone who A) I trust to be rational as much as myself, and B) I know started with the same prior as me, and C) I know cannot have seen the evidence that I have seen, and D) I know has updated on evidence independent of evidence I have seen.
They say O(H)=1:2.
Then I can infer that they updated from 1:6 to 1:2 by multiplying with a likelihood ratio of 3:1. And because C and D, I can update on that likelihood ratio in order to end up with a posterior of O(H)=6:1.
The equal weight view would have me adjust down, whereas Bayes tells me to adjust up.
I think there are several things wrong with the Equal Weight View, but I think this is the easiest way to see it:
Let’s say I have O(H)=2:1 which I updated from a prior of 1:6. Now I meet someone who A) I trust to be rational as much as myself, and B) I know started with the same prior as me, and C) I know cannot have seen the evidence that I have seen, and D) I know has updated on evidence independent of evidence I have seen.
They say O(H)=1:2.
Then I can infer that they updated from 1:6 to 1:2 by multiplying with a likelihood ratio of 3:1. And because C and D, I can update on that likelihood ratio in order to end up with a posterior of O(H)=6:1.
The equal weight view would have me adjust down, whereas Bayes tells me to adjust up.