How does this allow extracting money from CDTheorists?
Simple analysis:
If 0.75 is correct, and the prediction was of the form
a) Box A will not be chosen − 3 dollars in there
OR
b) Box B will not be chosen − 3 dollars in there
Then the CDTheorist reasons:
(1-0.75) = .25
.25*3 = .75
.75 − 1 = -.25
‘Therefore I should not buy a box—I expect to lose (expected) money by doing so.’
Complex analysis:
The seller generates a probability distribution over both boxes. (For simplicity’s sake, the buyer is chosen in advance, and given the chance to play.) If it is predicted neither box will be chosen, then BOTH boxes have $3 in them.
In this scenario will a CDTheorist buy? Should they?
>‘Therefore I should not buy a box—I expect to lose (expected) money by doing so.’
Well, that’s not how CDT as it is typically specified reasons about this decision. The expected value 0.25*3=0.75 is the EDT expected amount of money in box Bi for both i=1 and i=2. That is, it is the expected content of box Bi, conditional on takingBi. But when CDT assigns an expected utility to taking box Bi it doesn’t condition on taking Bi. Instead, because it cannot causally affect how much money is in box Bi, it uses its unconditional estimate of how much is in box Bi. As I outlined in the post, this must be at least $1.5.
How does this allow extracting money from CDTheorists?
Simple analysis:
If 0.75 is correct, and the prediction was of the form
a) Box A will not be chosen − 3 dollars in there
OR
b) Box B will not be chosen − 3 dollars in there
Then the CDTheorist reasons:
(1-0.75) = .25
.25*3 = .75
.75 − 1 = -.25
‘Therefore I should not buy a box—I expect to lose (expected) money by doing so.’
Complex analysis:
The seller generates a probability distribution over both boxes. (For simplicity’s sake, the buyer is chosen in advance, and given the chance to play.) If it is predicted neither box will be chosen, then BOTH boxes have $3 in them.
In this scenario will a CDTheorist buy? Should they?
>Then the CDTheorist reasons:
>(1-0.75) = .25
>.25*3 = .75
>.75 − 1 = -.25
>‘Therefore I should not buy a box—I expect to lose (expected) money by doing so.’
Well, that’s not how CDT as it is typically specified reasons about this decision. The expected value 0.25*3=0.75 is the EDT expected amount of money in box Bi for both i=1 and i=2. That is, it is the expected content of box Bi, conditional on taking Bi. But when CDT assigns an expected utility to taking box Bi it doesn’t condition on taking Bi. Instead, because it cannot causally affect how much money is in box Bi, it uses its unconditional estimate of how much is in box Bi. As I outlined in the post, this must be at least $1.5.