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.
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.