And since every summand includes a P(Odd n X) or a P(Even n X) everything is already multiplied with P(Even) or P(Odd) as appropriate. In retrospect it would have been a lot clearer if I had factored that out, but I wrote U_not_replace first in the way that seemed most obvious and merely modified that to U_replace so it never occured to me to do that.
Omega visits either the “odd” world or “even” world, not Odd world or Even world. For example, in Odd world it’d still need to decide between “odd” and “even”.
That’s what multiplying with P(“odd”|Odd) etc was about. (the probability that, given Omega appearing in an Odd world it would appear in an “odd” world). I thought I explained that?
But implicitly.
P(Omega_in_Odd_world)=P(Omega_in_Even_world)=0.5, but
P(Omega_in_Odd_world|Odd)= P(Omega_in_Even_world|Even)=1
And since every summand includes a P(Odd n X) or a P(Even n X) everything is already multiplied with P(Even) or P(Odd) as appropriate. In retrospect it would have been a lot clearer if I had factored that out, but I wrote U_not_replace first in the way that seemed most obvious and merely modified that to U_replace so it never occured to me to do that.
Omega visits either the “odd” world or “even” world, not Odd world or Even world. For example, in Odd world it’d still need to decide between “odd” and “even”.
That’s what multiplying with P(“odd”|Odd) etc was about. (the probability that, given Omega appearing in an Odd world it would appear in an “odd” world). I thought I explained that?