This still doesn't seem right to me. If a paper is the third paper, than the n-3 remaining papers will not have the same thing written on them as the 3d paper, and therefor it is less likely that I will observe whatever the 3d paper was than it was when I started. In the hat with replacement I have an even chance of seeing each one after I have observed it.
It stands to reason that if there were N papers, Y/N of them yeses, if I see and remove a y at the first trial, P(y_2|y_1) = Y-1/N-1 and this now becomes our prior and we use the same rule if we see another yes, if we ~yes, P(y_2|~y_1) = Y/N-1. Under this reasoning, it is clear that without replacement, as you remove yeses, you should expect nos more often because there are less yeses left.
Yes that is exactly the paradox I was having.
(edit):
Actually, Manfred seems to have solved the issue.
All in all a decent post I thought. Why can't i see the score?
He never said where it was, the problem was to find where the line was on the table.
Anybody else drink IPAs just cause they are cool? I know there's someone in here. I admit it: I hated it when I first tried it. And I would have never drank that bitter^10 garbage long enough to like it, if I didn't know it was hip first.
Maybe if it wasn't for people doing things cause they're hip, hard things to like at first with high future payoffs, would not even get as popular as they are today. AND THAT INCLUDES LW! Did you really love LW the first time you came across it? I did honestly fall in love with LW upon first contact, but I was already an aspiring rationalist with quite a radical take on the virtue of rationality.
So, should we care? I don't think so. Actually i think it might even be possible that we should make LW hipper. We perhaps should make EY the Fonz of rationality; and start wearing catchy uniforms; and start speaking a secret code, etc. if we really want LW style rationality to start to catch on in meat-space. The karma system already does well to motivate you and make you feel like a part of a community; but why not just go full on cult tactics? If it'll make people jealous, lets do it. Of course, we should always educate LWers about things you are supposed to like. But i see no good reason to turn down those that join LW because it's hip, or any reason why we shouldn't make it hipper, as long as we don't change the karma system it'll be good.
This feels wrong to me. But I don't know why. Wanna help me out.
Thanks :)