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A Proper Scoring Rule for Confidence Intervals
Neil Fitzgerald40

I think an algorithm for N outcomes is: spin twice, gain 1 every time you get the answer right but lose 1 if both guesses are the same.

One can "see intuitively" why it works: when we increase the spinner-probability of outcome i by a small delta (imagining that all other probabilities stay fixed, and not worrying about the fact that our sum of probabilities is now 1 + delta) then the spinner-probability of getting the same outcome twice goes up by 2 x delta x p[i]. However, on each spin we get the right answer delta x q[i] more of the time, where... (read more)

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2gjm
Just to be clear: if you spin twice and both come up right, you're gaining 2 and then losing 1? (I.e., this is equivalent to what you wrote in an earlier version of the comment?)