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westward comments on Open thread, August 26 - September 1, 2013 - Less Wrong Discussion
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I'm not strong enough in math to figure out how the scoring actually works without spending some time with it, and I wouldn't "throw" questions anyway. But I do like seeing that, say, on my 60%s I'm actually right 70% of the time. So when I'm feeling "60%" I should actually go with 70% more often. I think I'm afraid of getting questions wrong because the score penalty appears so high relative to the score bonus (I know that's likely appropriate, even though I don't understand the actual log bits, etc of scoring ).
The scoring is done so that if you have 70% of your answers right, then you get the best average score by guessing 70%, not 60%. The increased penalty you get for getting 30% of those answers wrong is smaller than the increased gain for getting 70% of them right.
But that's true only as long as you really get 70% of them right; so changing your answer e.g. to 80% while being only 70% correct would decrease the average score, because then the increased penalty for getting 30% of those answers wrong would be greater than the increased gain for getting the 70% right.
Without understanding the log bits, you can easily verify this in a spreadsheet calculator. Make a formula saying how many points you get if you report probability R and if you really get P answers right. Playing with numbers, you will find out that for a given P, you get the highest average score for R = P.