Re: copying related probability question

Wei Dai (
Tue, 23 Sep 1997 12:01:25 -0700 (PDT)

On Tue, 23 Sep 1997, Hal Finney wrote:

> 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.

First, the bet is wrong, it should be head up (not down) he loses 1/a2
dollars, else he wins 1/(1-a2). This way the subject has zero expected
profit. Suppose the subject accepts the bet, and remember that if the coin
landed head up, there would be two subjects who answer question 2. Then
if the coin landed head up, the experimenter wins 2/a2 dollars, otherwise
he loses 1/(1-a2) dollars. a2 should be 2/3 if the experimenter is to
have zero expected profit.

> 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.

No, I think the only way to avoid being taken advantage of is to answer
with answer set B. If the subject(s) answer 1/2 to question 2 the
experimenter will have a positive expected profit on what the subject(s)
think is a fair bet.