If Bob is as certain as Al that Bob was picked specifically for his result, then they do have the same information, and they should both discount Bob’s observations to the same degree for that reason.
Here’s why:
VARIANT 2: Charlie has both Al and Bob into his office before the drawings take place. He explains that the first guy (other than Al) to see 25⁄100 big will report to Al. Bob goes out and sees 25⁄100 big. To his surprise, he gets called into Charlie’s office and informed that he was the first to see that result.
Question: right now, what should Bob expect to hear from Al?
Intuitively, he should expect that Al had similar results. But if you’re right, it would seem that Bob should discount his results once he talks to Charlie and fights out that he is the messenger. If that’s right, he should have no idea what to expect Al to say. But that seems wrong. He hasn’t even heard anything from Al.
If you’re still not convinced, consider:
VARIANT 3: Charlie has both Al and Bob into his office before the drawings take place. He explains that the first guy (other than Al) to see 25⁄100 big will win a trip to Hawaii. Bob goes out and sees 25⁄100 big. To his surprise, he gets called into Charlie’s office and informed that he was the first to see that result.
I can see no grounds for treating VARIANT 3 differently from VARIANT 2. And it is clear that in VARIANT 3 Bob should not discount his results.
I’m not sure about this:
Here’s why:
VARIANT 2: Charlie has both Al and Bob into his office before the drawings take place. He explains that the first guy (other than Al) to see 25⁄100 big will report to Al. Bob goes out and sees 25⁄100 big. To his surprise, he gets called into Charlie’s office and informed that he was the first to see that result.
Question: right now, what should Bob expect to hear from Al?
Intuitively, he should expect that Al had similar results. But if you’re right, it would seem that Bob should discount his results once he talks to Charlie and fights out that he is the messenger. If that’s right, he should have no idea what to expect Al to say. But that seems wrong. He hasn’t even heard anything from Al.
If you’re still not convinced, consider:
VARIANT 3: Charlie has both Al and Bob into his office before the drawings take place. He explains that the first guy (other than Al) to see 25⁄100 big will win a trip to Hawaii. Bob goes out and sees 25⁄100 big. To his surprise, he gets called into Charlie’s office and informed that he was the first to see that result.
I can see no grounds for treating VARIANT 3 differently from VARIANT 2. And it is clear that in VARIANT 3 Bob should not discount his results.