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army1987 comments on What Bayesianism taught me - Less Wrong
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Well ... you can have an expected direction, just not if you account for magnitudes.
For example if I'm estimating the bias on a weighted die, and so far I've seen 2/10 rolls give 6's, if I roll again I expect most of the time to get a non-6 and revise down my estimate of the probability of a 6; however on the occasions when I do roll a 6 I will revise up my estimate by a larger amount.
Sometimes it's useful to have this distinction.
That's not what “expected” means in these contexts.
I'm well aware of this. My point was that there's a subtle difference between "direction of the expectation" and "expected direction".
The expectation of what you'll think after new evidence has to be the same as you think now, so can't point in any particular direction. However "direction" is a binary variable (which you might well care about) and this can have a particular non-zero expectation.
I'm being slightly ambiguous as to whether "expected" in "expected direction" is meant to be the technical sense or the common English one. It works fine for either, but to interpret it as an expectation you have to choose an embedding of your binary variable in a continuous space, which I was avoiding because it didn't seem to add much to the discussion.
Maybe 'on expectation' is clearer?