[goatlover]

No, that just means that some people ignore or discount objective facts for ideological reasons. The Earth is roughly a sphere, and that is empirically provable.

The arbiter should be well established science, history, math and logic. Of course there is still room for plenty of debate where the matter is not already settled by overwhelming evidence. That's where there shouldn't be an arbiter. But for factual matters like the Earth being (roughly) spherical, there's no actual debate. Just belief that goes contrary to the evidence.