Proper scoring rule

A proper scoring rule is a subset of scoring rules which incentivize the forecaster to report their true subjective probability distribution.

For the binary case, suppose a forecaster believes the outcome will occur with probability $$p$$ and reports belief $$b$$, which will be scored by the rule $$f$$. We call $$f$$ proper if $$E[f(b, x)]$$ is maximized when $$b = p$$. We call $$f$$ strictly proper if $$f$$ is proper and $$E[f(b, x)]$$ is maximized only for $$b = p$$.


 * Besiroglu, Tamay. Why it is rational to predict according to your true beliefs