And realistically, asking for probability distributions over unbounded sample spaces is trouble even for human experts. I suppose the space for "are mermaids real?" is workable (there are caveats like "yes but extinct", but yes/no is basically sufficient), but for anything subjective or political it's almost hopeless.

That said, this is a really interesting idea for behind-the-scenes work. The public might not want percentages, but I suspect experts could get some interesting results by diving into confidence levels and secondary answers.