= 27d567bc2d48d9f40e9ccc20ea370b15)
Dmytry comments on A (very) tentative refutation of Pascal's mugging - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (34)
If you flip a coin 15 times, this result:
HHHHHHHHHHHHHHH
is far more probable than this:
HTHTTHTHTTTHHTH
That's because some coins are rigged, and it's much easier to rig a coin to conform the first pattern than the second.
I suppose that isn't all that unintuitive (though does this actually work if you start with a uniform prior over weights and do the math?). But does your intuitive model also predict the fact that HTHTHTHTHT is more probable than HTHHTHTHTT? :D
Well, it is the case that all the random sequences together have much larger probability than HHHHHHHHHHHH , and so we should expect the sequence to be one among the random sequences.
edit: interesting issue: suppose you assign some prior probability to each possible sequence. Upon seeing the actual sequence, with probability that your eyes deceived you 0.0001, how are you to update the probability of this particular sequence? Why would we assume sensory failure (or a biased coin) when we observe hundred heads, but not something random-looking? It should have to do with the sensory failure being much less likely for something random looking.