This seems right, but I’m not confident I understand what’s meant by “P(I win at T2)”. I assume “I” is sampled out of the diagrammed entities (L2 and W2.1 … W2.N) existing at T2. With SIA or FTC, this is presumed to be uniform (even though the single L2 entity comes from one of two equiprobable universe-branches, and the N W2_N={W2.1...W2.N} all exist in the other). Is there some interpretation to “P(‘I’ win at T2)” other than this (i.e. P(“I” win at T2)=1-P(“I” is L2)=(under FTC)1-1/N) ?
The correct application of partitioning (that is, P(a)=P(a|b)P(b)+P(a|-b)P(-b)) to P(‘I’ win at T2) would be
P(‘I’ win at T2)=P(‘I’ is in {W2.1,...,W2.N})=P(‘I’ is not L2|‘I’ came from W1)P(‘I’ came from W1)+P(‘I’ is L2|‘I’ came from L1)P(‘I’ came from L1).
(since ‘I’ came from L1 is the negation of ‘I’ came from W1)
Note that this doesn’t save us from choosing what distribution to sample ‘I’ (at T2) from—we can still use SIA/FTC.
BOP is definitely punning “I” (which turns out to give a correct answer only under the particular rule for assigning to “I” where P(“I” is L2)=1/2).
This seems right, but I’m not confident I understand what’s meant by “P(I win at T2)”. I assume “I” is sampled out of the diagrammed entities (L2 and W2.1 … W2.N) existing at T2. With SIA or FTC, this is presumed to be uniform (even though the single L2 entity comes from one of two equiprobable universe-branches, and the N W2_N={W2.1...W2.N} all exist in the other). Is there some interpretation to “P(‘I’ win at T2)” other than this (i.e. P(“I” win at T2)=1-P(“I” is L2)=(under FTC)1-1/N) ?
The correct application of partitioning (that is, P(a)=P(a|b)P(b)+P(a|-b)P(-b)) to P(‘I’ win at T2) would be
P(‘I’ win at T2)=P(‘I’ is in {W2.1,...,W2.N})=P(‘I’ is not L2|‘I’ came from W1)P(‘I’ came from W1)+P(‘I’ is L2|‘I’ came from L1)P(‘I’ came from L1).
(since ‘I’ came from L1 is the negation of ‘I’ came from W1)
Note that this doesn’t save us from choosing what distribution to sample ‘I’ (at T2) from—we can still use SIA/FTC.
BOP is definitely punning “I” (which turns out to give a correct answer only under the particular rule for assigning to “I” where P(“I” is L2)=1/2).