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Mark_Gomer comments on Rationality quotes: May 2010 - Less Wrong
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I dig what you've done, but as a mathematician, my instinct would be to do calculations like this with variables instead of made-up numbers... that way you can be sure that your results hold In General.
Sure, I just couldn't be bothered. If you ignore the complicating factor of having black balls in the white urn and vice-versa (i.e. we look at the problem where the urn is 100% white or 100% black). then the maths is easier, and we can quickly see that this always holds whatever variables we put in.
In fact, it also works for many different scoring algorithms. If our scoring algorithm is f(x) then it the proof works whenever xf(x)+(1-x)f(1-x) is increasing on [0.5,1].As far as I can tell this happens all of the time that f(x) is increasing on [0,1].