there is no logical update on what it does after you know your own decision.
Consider Newcomb’s Dilemma with an imperfect predictor Psi. Psi will agree with Omega’s predictions 95% of the time.
P($1000000 in B | you choose to one-box) = .95
P($0 in B | you choose to two-box) = .95
Utility of one boxing: .95 1000000 + .05 0= $950,000
Utility of two boxing: .95 1000 + .05 1000000 = $50,950
Now, lets say that Psi just uses Omega’s prediction on the person most similar to you (lets call them S), but there’s a 95% chance that you disagree with that person.
P($1000000 in B | S chooses to one-box) = 1
P($0 in B | S chooses to two-box) = 1
and
P(S chooses to one-box | you choose to one-box) = .95
P(S chooses to two-box | you choose to two-box) = .95
You’ll find that this is the same as the situation with Psi, since
P($1000000 in B | you choose to one-box) = P($1000000 in B | S chooses to one-box) P(S chooses to one-box | you choose to one-box) = 1 .95 = .95.
Since the probabilities are the same, the expected utilities are the same.
Now, lets use evolution as our predictor. Evolution is unable to model you, but it does know what your parents did.
However, you are not your parents. I will be liberal though, and assume that you have a 95% chance of choosing the same thing as them.
So,
P(you one-box | your parents one-boxed) = .95
P(you two-box | your parents two-boxed) = .95
Since Evolution predicts that you’ll do the same thing as your parents,
P($1000000 in B | your parents one-boxed) = 1
P($0 in B | your parents two-boxed) = 1
This may seem similar to the previous predictor, but there’s a catch—you exist. Since you exist, and you only exist because your parents one-boxed,
Note how the fact of your existence implies that your parents one boxed. Though you are more likely to choose what your parents chose, you still have the option not to.
Calculate the probabilities:
P($1000000 in B) = P($1000000 in B | your parents one-boxed) P(your parents one-boxed) + P($1000000 | your parents two-boxed) P(your parents two-boxed)= 1 1 0 0= 1
and P($0 in B) = 0
Since you exist, you know that your parents one-boxed. Since they one-boxed, you know that Evolution thinks you will one-box. Since Evolution thinks you’ll one box, there will be $1000000 in box B. Most people will in fact one-box (just in this model), just because of that 95% chance that they agree with their parents thing, but the 5% who two box get away with an extra $1000.
So basically, once I exist I know I exist, and Evolution can’t take that away from me.
Also, please feel free to point out errors in my math, its late over here and I probably made some.
Consider Newcomb’s Dilemma with an imperfect predictor Psi. Psi will agree with Omega’s predictions 95% of the time.
P($1000000 in B | you choose to one-box) = .95
P($0 in B | you choose to two-box) = .95
Utility of one boxing: .95 1000000 + .05 0= $950,000
Utility of two boxing: .95 1000 + .05 1000000 = $50,950
Now, lets say that Psi just uses Omega’s prediction on the person most similar to you (lets call them S), but there’s a 95% chance that you disagree with that person.
P($1000000 in B | S chooses to one-box) = 1
P($0 in B | S chooses to two-box) = 1
and
P(S chooses to one-box | you choose to one-box) = .95
P(S chooses to two-box | you choose to two-box) = .95
You’ll find that this is the same as the situation with Psi, since P($1000000 in B | you choose to one-box) = P($1000000 in B | S chooses to one-box) P(S chooses to one-box | you choose to one-box) = 1 .95 = .95.
Since the probabilities are the same, the expected utilities are the same.
Now, lets use evolution as our predictor. Evolution is unable to model you, but it does know what your parents did.
However, you are not your parents. I will be liberal though, and assume that you have a 95% chance of choosing the same thing as them.
So,
P(you one-box | your parents one-boxed) = .95
P(you two-box | your parents two-boxed) = .95
Since Evolution predicts that you’ll do the same thing as your parents,
P($1000000 in B | your parents one-boxed) = 1
P($0 in B | your parents two-boxed) = 1
This may seem similar to the previous predictor, but there’s a catch—you exist. Since you exist, and you only exist because your parents one-boxed,
P(your parents one-boxed | you exist) = 1
P(your parents one-boxed) = 1 and P(your parents two-boxed) = 0.
Note how the fact of your existence implies that your parents one boxed. Though you are more likely to choose what your parents chose, you still have the option not to.
Calculate the probabilities:
P($1000000 in B) = P($1000000 in B | your parents one-boxed) P(your parents one-boxed) + P($1000000 | your parents two-boxed) P(your parents two-boxed)= 1 1 0 0= 1
and P($0 in B) = 0
Since you exist, you know that your parents one-boxed. Since they one-boxed, you know that Evolution thinks you will one-box. Since Evolution thinks you’ll one box, there will be $1000000 in box B. Most people will in fact one-box (just in this model), just because of that 95% chance that they agree with their parents thing, but the 5% who two box get away with an extra $1000.
So basically, once I exist I know I exist, and Evolution can’t take that away from me.
Also, please feel free to point out errors in my math, its late over here and I probably made some.