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JoshuaZ comments on What Bayesianism taught me - Less Wrong
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Here's a situation where an anecdote should reduce our confidence in a belief:
If this person were to offer an anecdote, it should reduce our confidence in his proposition, because it makes it unlikely he knows of stronger supporting evidence.
I don't know how applicable this is to actual people.
I don't think this is necessarily valid, because people also know that anecdotes can be highly persuasive. So for many people, if you have an anecdote it will make sense to say so, since most people argue not to reach the truth but to persuade.