That weirdness is kinda just a consequence of wanting the scores for different questions to be added together. A simpler (to me) but equivalent way to frame it

That weirdness is kinda just a consequence of wanting the scores for different questions to be added together. A simpler (to me) but equivalent way to frame it is to use scores that you multiply together. These scores are "the probability of the true answer occur, assuming the students odds." That is, if the student gave a probability of 1 and were correct, their score for that question is 1. If they were wrong, they get a score of zero. The interpretation of their final score his interpreted simillarly as a joint probability, assuming independent trials.