There’s a sense in which what I said is true (see ygert’s comment), but I agree it’s confusing. Suggested re-word? Or maybe I should just cut that point.
You should expect that, on average, a test will leave your beliefs unchanged.
That happens to be not true. A test which ouputs useful information WILL change your beliefs. Especially given point 2, one can say “Any informative test will always change your beliefs”.
What’s tricky here is expectation. You expect your beliefs to change but you don’t know in which direction. So your expectation is for zero change even though you know that you’ll get some non-zero change.
This looks paradoxical, but is the entirely standard way in which statistics (in particular random variables) operate. Consider a toss of a fair coin. The expectation is half heads half tails which is guaranteed not to happen. You know you’ll get either heads or tail but not which one of those two. The expectation will not match the outcome—all it can do is be equidistant (appropriately weighted) from all possible outcomes.
Your expectation of the possible beliefs you could have after seeing the test results should match your current belief.
Another option is to try to illustrate both CoEE and Beliefs Pay Rent in Anticipated Experiences at the same time, since I think failing BPRiAE demonstrates an easy way to fail CoEE.
There’s a sense in which what I said is true (see ygert’s comment), but I agree it’s confusing. Suggested re-word? Or maybe I should just cut that point.
I think that problem is in the sentence
That happens to be not true. A test which ouputs useful information WILL change your beliefs. Especially given point 2, one can say “Any informative test will always change your beliefs”.
What’s tricky here is expectation. You expect your beliefs to change but you don’t know in which direction. So your expectation is for zero change even though you know that you’ll get some non-zero change.
This looks paradoxical, but is the entirely standard way in which statistics (in particular random variables) operate. Consider a toss of a fair coin. The expectation is half heads half tails which is guaranteed not to happen. You know you’ll get either heads or tail but not which one of those two. The expectation will not match the outcome—all it can do is be equidistant (appropriately weighted) from all possible outcomes.
I might go with:
Another option is to try to illustrate both CoEE and Beliefs Pay Rent in Anticipated Experiences at the same time, since I think failing BPRiAE demonstrates an easy way to fail CoEE.