• Appropriate authority:Expert.
• Expert: Person whose opinions are worth something.

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.

How is 'everyone an authority' different from 'there are no authorities?'

Well, using your definition of authority as "person with opinions that others agree with", these statements would translate as follows:
- 'everyone is an authority' becomes "Every person has opinions that others agree with."
- 'there are no authorities' becomes "No person has opinions that others agree with."

The problem is that you seem to want to use the connotations of the word "authority", but you aren't explicitly including them in your definition.

What's your definition?.

I don't use the word 'authority' in reference to people, because it communicates meaning badly. I'd prefer to use a word like 'expert' or a phrase like 'informed on the subject'.