billswift comments on Bead Jar Guesses - Less Wrong

17 Post author: Alicorn 04 May 2009 06:59PM

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Comment author: Cyan 04 May 2009 08:43:30PM *  0 points [-]

I see this conclusion as a mistake...

... but it isn't, because the degree of surprise doesn't just depend on the raw probability, but also only the number of other possible outcomes under consideration. That Omega uses the term "lilac" may reasonably be taken as evidence that the space of color outcomes should be treated as finely divided.

ETA: I guess the mistake is in comparing feelings of surprise across outcomes with the same probability embedded in event spaces with different cardinalities.

Comment author: billswift 04 May 2009 10:05:58PM 0 points [-]

"doesn't just depend on the raw probability" - Correct. It also depends strongly on how reliable you think your estimate of the probability is. That is, your confidence interval.