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Adele_L comments on Open thread, September 2-8, 2013 - Less Wrong Discussion
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Is there a name for, taking someone being wrong on A as evidence as being wrong on B? Is this a generally sound heuristic to have? In the case of crank magnetism; should I take someone's crank ideas, as evidence against an idea that is new and unfamiliar to me?
Bayes' theorem to the rescue! Consider a crank C, who endorses idea A. Then the probability of A being true, given that C endorses it equals the probability of C endorsing A, given that A is true times the probability that A is true over the probability that C endorses A.
In equations: P(A being true | C endorsing A) = P(C endorsing A | A being true)*P(A being true)/P(C endorsing A).
Since C is known to be a crank, our probability for C endorsing A given that A is true is rather low (cranks have an aversion to truth), while our probability for C endorsing A in general is rather high (i.e. compared to a more sane person). So you are justified in being more skeptical of A, given that C endorses A.