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Mark_Neznansky comments on Epistemic vs. Instrumental Rationality: Approximations - Less Wrong
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When I'm choosing between approximations, I haven't actually started using the approximation yet. I'm predicting, based on the full knowledge I have now, the cost of replacing that full knowledge with an approximation.
So to calculate the expected utility of changing my beliefs (to the approximation), I use the approximation to calculate my hypothetical actions, but I use my current beliefs as probabilities for the expected utility calculation.
It seems to me you use wrong wording. In contrary to the epistemic rationalist, the instrumental rationalist does not "gain" any "utility" from changing his beliefs. He is gaining utility from changing his action. Since he can either prepare or not prepare for a meteoritic catastrophe and not "half prepare", I think the numbers you should choose are 0 and 1 and not 0 and 0.5. I'm not entirely sure what different numbers it will yield, but I think it's worth mentioning.
Why does it sound more like 1 than .5? If I believed the probability of my home getting struck by a meteorite was as high as .5, I would definitely make preparations.