When fallacies don’t matter

The United States Supreme Court has discussed the prosecutor’s fallacy in McDaniel v Brown [2010] USSC No 08-559, 11 January 2010. After several different explanations of what this fallacy is, the Court held that in this particular case the probabilities were such that even on the numbers most favourable to the accused (Mr Brown) the jury had not been wrong to convict him. The case concerned DNA so of course – to put it in Bayesean (or, if you like, Bayesian) terms which are clearer than those used by the Court – in the absence of an innocent explanation for his DNA being at the scene the denominator of the likelihood ratio was small, the ratio large, and the probative value of the evidence large.

This illustrates the point that errors in reasoning do not always matter. Hopefully this will not encourage expert witnesses to avoid accurate thinking.

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