# ygert comments on Bayesianism for Humans - Less Wrong

52 29 October 2013 11:54PM

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Comment author: 29 October 2013 11:55:47AM *  9 points [-]

You should expect that, on average, a test will leave your beliefs unchanged.

Emphasis mine.

When I shake the box, my belief that the coin landed heads is 50%. When I look inside, my belief changes, yes, but two one of two options of equal probability: 0% (I see it came out tails), or 100% (I see it came out heads.)

It is trivial to see that my expected posterior belief is 0% * 1/2 + 100% * 1/2 = 50%, or in other words, it's exactly equal to my prior belief.

Comment author: 30 October 2013 01:30:16PM 4 points [-]

The question is whether 'change' signifies only a magnitude or also a direction. The average magnitude of the change in belief when doing an experiment is larger than zero. But the average of change as vector quantity, indicating the difference between belief after and before the test, is zero.

If you drive your car to work and back, then the average velocity of your trip is 0, but the average speed is positive.