Re: copying related probability question

Hal Finney (
Tue, 23 Sep 1997 07:48:14 -0700

Here is another paradox. Wei wrote:

> 1. If the subject's answer to question 3 is a3, then he should be willing
> to accept the following bet after giving his answer: if the coin landed
> up, he loses 1/a3 dollars, else he wins 1/(1-a3) dollars. But if a3<1/2,
> the experimenter has a positive expected profit from running the
> experiment.

(For reference, question 3 is "given that you are not a clone, did the
coin land heads".)

Consider question 2, "did the coin land heads". Suppose the subject's
answer to that is a2. He should be willing to accept the bet: if the coin
landed heads down, he loses 1/a2 dollars, else he wins 1/(1-a2) dollars.
But if a2>1/2, the experimenter again has a positive expected profit.

The reasoning which leads to answer (B) gives a2 = 2/3. So in this case,
too, the experimenter can make a profit off the hapless clonee.

Apparently whichever line of reasoning the subject uses, the experimenter
can take advantage of him. The only way to avoid it is for the subject
to answer both questions 2 and 3 as 1/2.