Sum to 0 if probabilities are nonnegative scalars seem to be cumbersome. If probabilities are mathematical entities that are free to choose, the sum to 0 "can b

Sum to 0 if probabilities are nonnegative scalars seem to be cumbersome. If probabilities are mathematical entities that are free to choose, the sum to 0 "can be played" by quite a few abelian groups. I think it's especially important to be able to make a distinction between truth and falsehood however. If they are both 0, this is difficult. :-)