is the log odds of the probability assigned to the correct outcome a proper scoring rule?
@niplav Let p = the probablity you assign to the true outcome, and q = the probablity you write down. Then your expected score is s(p,q) = p f(q) + (1-p) f(1-q) where f(q) is the score awarded when assigning a probablity of q to the correct outcome.
If the scoring rule is proper, then the derivative would be 0 when p = q. This is not the case for points based on the log odds: https://www.wolframalpha.com/input?i=d%2Fdq+%28p+ln%28q%2F%281-q%29%29+%2B+%281-p%29+ln%28%281-q%29%2Fq%29+%29%3D+0
