Starting this discussion, I gave a probability of one in a million. After reading up on the subject further, I found a physicist who said one in fifty million, and am willing to bow to his superior expertise.
Was there only a one in fifty chance my probability would change this much? This doesn’t seem right, because I knew going in that I knew very little about the subject and if you’d asked me whether I expected my probability to change by a factor of at least fifty, I would have said yes (though of course I couldn’t have predicted in which direction).
It seems to me it would be fine for David to believe with high probability that he would get new evidence that would change his probability to 3E12, as long as he believed it equally possible he’d get new evidence that would change it to 3E32
A 1/3e22 probability means you believe there’s a 1/3e22 chance of the event happening.
If you have, for example a 1/1e9 chance of finding evidence that increases that to 1/3e12, then you have a 1/1e9*1/3e12 chance of the event happening.
Which is 1/3e21.
So, in order to be consistent, you must believe that there is, at most, a 1/1e10 chance of you finding evidence that increases the probability to 1/3e12.
At which point, the probability of losing your rationality is obviously higher.
Yes. Yvain’s 1 in 50 million example, on the other hand, is fine, because the probability went down. In a more extreme example, it could have had a 50-50 chance of going down to 0 (dropping by a factor infinity) as long as there had been a 50-50 chance of it doubling. Conservation of expected evidence.
Okay, now I’m confused, or misunderstanding you.
Starting this discussion, I gave a probability of one in a million. After reading up on the subject further, I found a physicist who said one in fifty million, and am willing to bow to his superior expertise.
Was there only a one in fifty chance my probability would change this much? This doesn’t seem right, because I knew going in that I knew very little about the subject and if you’d asked me whether I expected my probability to change by a factor of at least fifty, I would have said yes (though of course I couldn’t have predicted in which direction).
It seems to me it would be fine for David to believe with high probability that he would get new evidence that would change his probability to 3E12, as long as he believed it equally possible he’d get new evidence that would change it to 3E32
A 1/3e22 probability means you believe there’s a 1/3e22 chance of the event happening.
If you have, for example a 1/1e9 chance of finding evidence that increases that to 1/3e12, then you have a 1/1e9*1/3e12 chance of the event happening.
Which is 1/3e21.
So, in order to be consistent, you must believe that there is, at most, a 1/1e10 chance of you finding evidence that increases the probability to 1/3e12.
At which point, the probability of losing your rationality is obviously higher.
Yes. Yvain’s 1 in 50 million example, on the other hand, is fine, because the probability went down. In a more extreme example, it could have had a 50-50 chance of going down to 0 (dropping by a factor infinity) as long as there had been a 50-50 chance of it doubling. Conservation of expected evidence.