This scoring rule does not depend only on the probability at the actually occuring value. You dont even report the probability at any value. I am not trying to incentivize reporting of probabilities of specific value, I am trying to incentivize reporting an interval such that the person reporting the belief believes the point will lie in with probability 90%.
Your rule seems to be trying to do something else, but it will not incentivize me giving my 90% confidence interval in cases where my beliefs are not normally distributed.
This scoring rule does not depend only on the probability at the actually occuring value. You dont even report the probability at any value. I am not trying to incentivize reporting of probabilities of specific value, I am trying to incentivize reporting an interval such that the person reporting the belief believes the point will lie in with probability 90%.
Your rule seems to be trying to do something else, but it will not incentivize me giving my 90% confidence interval in cases where my beliefs are not normally distributed.