At the risk of repeating myself I’ll weigh in here: X is an authority with respect to a proposition P to the extent that X’s assertion of P is evidence for P.
On many topics, some people’s assertions are stronger evidence than others. That makes those people authorities on those topics, relatively speaking.
To my mind, the interesting question is how we best distinguish actual authorities on a topic from people who merely claim authority. That’s difficult. But the first step in learning distinguish among A and B is to acknowledge that A and B actually are different things: in this case, that actual authorities on a topic are a distinct thing in the world from non-authorities.
Asserting that there are no authorities, or that everyone is equally authoritative, is a step in the wrong direction.
You know what, if you were to actually have to program a conclusion-drawing machine, not just philosophize about it, I’d bet that your decision algorithm in which conclusions are drawn “based upon the rationality of their assertions alone” would be indistinguishable from a decision algorithm in which conclusions are based on “‘evidence’ (which are opinions)”.
You might name the functions differently through, you might have a “concludeBasedOnRationailty()” function instead of a “concludeBasedOnEvidence()” function. I bet it would still translate into the same code, because there’s not a single word you’ve stated that relates to anything other than how we name things.