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Vaniver comments on 2014 Survey Results - Less Wrong
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The primary property you want to maintain with a scoring rule is that the best probability to provide is your true probability. I know that the Bayes score generalizes to multiple choice questions, which implies to me that it most likely works with a multiplicity for wrong answers, so long as the multiplicity is close to the actual multiplicity.
I think the primary property you want to maintain is that it's best to provide the answer you consider most likely, otherwise it's best to say 'sdfkhasflk' - 0% to all of them you aren't certain of.
Multiple choice would making the scoring clearer, but that constraint could well make the calibration easier.