Open Thread: July 2010

komponisto

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

Part 2

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

Part 2

Interesting problem!

(This would be especially puzzling, since they have ALL the same information, having shared everything.)

It isn't terribly clear why Bob should discount all of his observations, since they don't seem to subject to any observation selection effect; at least from his perspective, his observations were a genuine random sample.

I think these two statements are inconsistent. 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. If Bob doesn't trust Al completely, they don't have the same information. Bob doesn't know for sure that Charlie told Al about the selection. From his point of view, Al could be lying.

VARIANT: as before, but Charlie has a similar conversation with Bob. Only this time, he tells him he's going to introduce Bob to someone who observed exactly 75 of 100 fish to be big.

If Charlie tells both of them they were both selected, they have the same information (that both their observations were selected for that purpose, and thus give them no information) and they can only decide based on their priors about Charlie stocking the pond.

If each of them only knows the other was selected and they both trust the other one's statements, same thing. But if each puts more trust in Charlie than in the other, then they don't have the same information.

I'm not sure about this:

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.

Questio... (read more)

1prase16y

It is strange. Shall Bob discount his observation after being told that he is selected? What does it actually mean to be selected? What if Bob finds 25 big fish and then Charlie tells him, that there are 3^^^3 other observers and he (Charlie) decided to "select" one of those who observe 25 big fish and talk to him, and that Bob himself is the selected one (no later confrontation with AI). Should this information cancel the Bob's observations? If so, why?