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thomblake comments on Shut Up And Guess - Less Wrong
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Presumably, as long as you're not equivocating on 'expected', that isn't true. For tests, 'test score'=='utility', no?
For an exam where what matters is your grade relative to other test-takers, like the SAT, probably yes, but on an exam with a hard pass/fail threshold, the utility function is discontinuous (and therefore non-linear) around the threshold, so guessing might make a difference.
Ah, good point. I always forget 'get the highest score possible' isn't everyone's goal; presumably, some people would prefer 70% and 100% about equally in this case.
It is about the 'expected' part. The average of utilities for each score does not have to equal the utility of the average score. It is only equal when utility scales linearly with score.