Add-on:
You can make the analogy clearer if you imagine, instead of rummaging around in a hat, you lined up all the strips of paper in random order and read them one at a time. Then it makes sense that the total number of slips of paper shouldn't matter.
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(y2|y1) = 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(y2|~y1) = 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.
This sounds like Bernouilli's urn. If you have N papers/balls, only one of which is Yes, then on every draw, your expectation is 1/N, right? and as you keep drawing, N gets smaller by 1 every turn.
In other words, as we keep drawing without hitting Yes, the odds of hitting Yes keep changing and getting more: 1/N, 1/N-1, 1/N-1-1, 1/N-1-1-1...
But in Laplace's Law, every day that goes by with the sun rising, N gets bigger since here N is the number of days that have passed, not how many days are left to go; the odds that the sun won't rise keep changing and getting less, 1/N, 1/N+1, 1/N+1+1, 1/N+1+1+1...
Unless I am missing something, Laplace's law is not like your papers-in-hat/Bernouilli-urn example.
Yes that is exactly the paradox I was having.
(edit):
Actually, Manfred seems to have solved the issue.
This is a question really, not a post, I just can't find the answer formally. Does laplace's rule of succession work when you are taking from a finite population without replacement? If I know that some papers in a hat have "yes" on them, and I know that the rest don't, and that there is a finite amount of papers, and every time I take a paper out I burn it, but I have no clue how many papers are in the hat, should I still use laplace's rule to figure out how much to expect the next paper to have a "yes" on it? or is there some adjustment you make, since every time I see a yes paper the odds of yes papers:~yes papers in the hat goes down.
All in all a decent post I thought. Why can't i see the score?
It may be that the rule that the emerald construction sites use to get either a green or non-green emerald change at time T, but there is no reason to believe that the rule will change if there has never been any change demonstrated in the position of the line before
There's your error! You think that the line is in the middle of the table through the entire experiment, but actually it's in the riddle of the table, where "riddle" means "in the middle of the table before time T and on the right side of the table afterward." All of our experience before time T has confirmed this.
He never said where it was, the problem was to find where the line was on the table.
definition of 'successful'
Generally this means the opposite of 'failed'. 'Was a good idea' is orthogonal to 'successful'; something can be either one without being the other. You're playing silly games by implicitly defining 'successful' as 'increased happiness' and then pretending this means anything.
and stop wire-heading when ever they want
I've never heard of a form of wireheading in which this was possible.
Are you new man? Check this out: http://wiki.lesswrong.com/wiki/A_Human%27s_Guide_to_Words
Potato is proposing a deffenition as an emperical pointer. It means plenty, it means when people think "success", they think "happiness up". He's just saying that the probabilities of the application of the two phrases are correlated to some significant degree.
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.
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The reason it seems that way is because you are imagining holding the number of Ys constant. However, if the number of Ys is unknown, you have to figure out what proportion of the cards say Y as you go along, so you get a different result.
Maybe an analogy will help. Because you draw the slips of paper in random order, they will not be correlated with each other except through the total percentages that say Y and N. Analogously, if you flip a weighted coin, the flips will not be correlated with each other except through the bias of the coin. Drawing a slip of paper follows the exact same mathematical rules as flipping a weighted coin. And so since Laplace's rule of succession works for the weighted coin, it also works for the slips of paper.
Since you're already thinking about keeping the number of Ys fixed, you may object, "but the number of Ys is fixed in the case of the papers and not fixed in the case of the coin, so they must be different." So we can go a step further and imagine someone else flipping the coin, and then writing down what they get. Now when we read the papers, there is a fixed number of Ys, but since it's the same coinflips all along, the probability of seeing Y or N is exactly the same. This demonstrates that having a finite amount of stuff doesn't really matter, what matters is the mathematical rules that stuff follows.
Thanks :)