Abstract Scoring rules measure the deviation between a forecast, which assigns degrees of confidence to various events, and reality. Strictly proper scoring have property that for any mathematical expectation score forecast p by lights is strictly better than other q . Forecasts need not satisfy axioms probability calculus, but Predd et al. [9] shown given finite sample space additive continuou...

Non-additive probability goes back to the very beginning of probability theory— the work of Jacob Bernoulli. Bernoulli’s calculus for combining arguments allowed both sides of a question to attain only small or zero probability, and he also thought the probabilities for two sides might sometimes add to more than one (Shafer 1978). Twentieth-century non-additive probability has roots in both mat...