Newcomb's Problem

$1,000,000 ($M) or $0	$1,000 ($T) for sure

Two choices:

S -- take the single box on the left

B -- take both boxes

The catch:

A Predictor who is 99% likely to guess your choice will either

s -- predict you choose S and place $M in the "?" box, or
b -- predict you choose B and leave the "?" box empty.

When you make your choice, the Predictor will already have made his prediction and (according to that prediction) either filled the "?" box with $M or left it empty.

Strategies:

Evidential Expected Utility (EEU) Strategy:

It's easy. Almost all (99%) of those who choose S walk away millionaires. Pick S.

EEU(S) = pr($M/S)U($M) + pr($0/S)U($0) = .99($M) + 0 = $990,000
EEU(B) = pr($MT/B)U($MT) + pr($T/B)U($T) = .01($MT) + .99($T) = $11,000

Causal Expected Utility (CEU) Strategy:

It's easy. Either the $M is in the "?" box or it isn't. If it is, you may as well have the $T, too. If it isn't, you'll want the $T. Pick B.

CEU(S) = pr(S $M)U($M) + pr(S $0)U($0)
CEU(B) = pr(B $MT)U($MT) + pr(B $T)U($T)

where pr(S $M) = pr(B $MT)
and pr(S $0) = pr(B $T)

CEU(B) = CEU(S) + $T

[On Skyrms' version of CEU, CEU(S) = pr(b) ($M), and CEU(B) = pr(b)($M) + $T.]

S $M means "If I choose S then I will get the $M."

HOW WOULD YOU CHOOSE?

Click HERE for my answer.

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