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Morendil comments on The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom - Less Wrong

42 Post author: komponisto 13 December 2009 04:16AM

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Comment author: Morendil 13 December 2009 09:12:53PM 3 points [-]

Can you explain your reasoning here, in terms of P(other folks' DNA on clasp|Sollecito guilty) vs P(other folks' DNA on clasp|Sollecito not guilty) ?

I can understand how this fact might be "suggestive" of something, but "suggestive" is the same kind of thinking as "suspicious": it's narrative rather than analytical.

Comment author: mattnewport 13 December 2009 11:47:45PM *  10 points [-]

It seems to me that the prosecution's case against Sollecito relies quite heavily on the evidence they claim proves he was present at the crime scene since they have no other solid evidence against him.

The reasoning used by the prosecution is basically what Jaynes calls the 'policeman's syllogism' in Probability Theory: The Logic of Science. The reasoning is of the form:

  • If A is true, then B becomes more plausible
  • B is true
  • Therefore, A becomes more plausible

Here A is (Sollecito was present at the crime scene) and B is (DNA tests on the bra clasp detected Sollecito's DNA). If we use C to stand for our background knowledge then by Bayes theorem:

p(A|BC) = p(A|C) * (p(B|AC) / p(B|C))

The premise of the policeman's syllogism "If A is true, then B becomes more plausible" takes the form

p(B|AC) > p(B|C)

And by Bayes theorem if this premise is true then:

p(A|BC) > p(A|C)

as stated in the syllogism. Now the significance of the evidence B depends on the magnitude of p(B|C) - the only way finding B to be true can greatly increase the plausibility of A is if p(B|C) is very small relative to p(B|AC). In other words, the prosecution's argument rests on the background probability of finding Sollectio's DNA on the bra clasp being very low relative to the probability of finding it if he were present at the crime scene.

Now it seems to me that the fact that the DNA of several other unidentified individuals (who it is not suggested were present at the crime scene) was also found on the bra clasp indicates that p(B|C) is not so much smaller than p(B|AC). B is only strong evidence for A if DNA on the clasp is much more likely if the person was present at the crime scene but we have several counter examples of DNA on the clasp from individuals who were not at the crime scene so we have reason to doubt that p(B|AC) is much greater than p(B|C) and therefore reason to doubt the significance of the evidence.

Comment author: Morendil 14 December 2009 07:24:38AM 1 point [-]

Now that is analytical.

And by and large I agree with the analysis - that is, I agree that how much weight to give to that particular evidence is determined by your estimates of P(B|AC) and p(B|C).

We may yet disagree on these, but if we do it should be on the basis of models that further evidence can in principle confirm or rule out, for instance whose DNA exactly was found on the clasp - does it match the investigators' ? They were at the crime scene. Contamination of that sort would help (in a Bayesian sense) the prosecution, not the defense.

What I take issue with is to say that something "does not count" when we have a previous commitment to take into account every bit of evidence available to us. Either we use Bayesian standards of inquiry, or judicial standards of inquiry, but we do not cherry-pick which is convenient to a given point we want to make.

Comment author: Cyan 14 December 2009 03:26:08AM 1 point [-]

Very well said.