I thought about averaging the scores, which gives you a point inside the circle, and then projecting onto the circle with a ray from the centre, which is continuous everywhere apart from where the average is at the centre (e.g. for two voters this is when they have exactly opposite views).
So if you have a continuous probability distribution on the domain the probability of undecidability has measure zero.
It's not the undecidability that is a problem, it's the discontinuity. Undecidable answers are manageable, random answers however are very annoying to deal with.
