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'.

Authority: person with opinions that others agree with.

Then far from saying that "there are no authorities", you ought have said "everyone is an authority", since every person has at least some opinions that other people agree with. (I at least don't know of anyone who is wrong about absolutely everything, so by that definition I consider everyone an authority)

I'll note that this is not a typical usage of the word 'authority' and therefore I'll not be using it in the future as it can only create confusion, not communicate meaning decently.

This again seems like just a definitional issue, of how to define 'authority', and I'll suggest to everyone not to be tempted to use different definitions as if they're matters of actual disagreement.

Nobody here believes in the existence of absolute authorities whose word would trump any amount of other evidence -- but even random people off the street might have opinions on a subject that could be considered 'Bayesian evidence' towards a conclusion; very slim evidence but evidence nonetheless.

Authority is almost always used to describe argumentation based on sources other than logic or evidence.

I don't think that's true. Most uses of "authority" are not about argumentation at all. The local parking authority, for existence.

Authority is practically meaningless as a concept if it includes both accurate and inaccurate foundations of argumentation. Probability theory works, appeals to authority don't.

I'm not sure this even makes sense enough to be wrong. I can't parse "accurate and inaccurate" with respect to "foundations of argumentation". Are you meaning to refer to fallacies, or something?

In general, there's nothing wrong with appeals to authority. It's well-understood that there is no formal logical step that takes one from "Authority says x" to "x". Nonetheless, TheOtherDave has it right:

X is an authority with respect to a proposition P to the extent that X's assertion of P is evidence for P.

It's worth remembering that other evidence screens off authority, but you have to take the evidence that you can get.

I was hoping to enter into dialog, but obviously my ideas are not welcome. I'll just go finish the conversations here: http://monkeyminds.hubpages.com/hub/Critiquing-Less-Wrong

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You may be correct about your own ability to understand anything that a superintelligence understands. I don't know you, and it would not be polite of me to speculate about that. But based on my own experiences, I'm rather confident that I don't have that ability. I'm also rather confident that there are tools that increase my ability to reason effectively.