komponisto
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- Jan 1, 2011
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So the question to Bayesians: if a priori is 0.97, and the probability of Knox being guilty solely based on case details is judged to be 0.05, what is the resulting probability?
Excellent question, actually. There's a very important probability-theoretic point here.
Kevin gave you the following response:
If 95% of fuzzballs are blue, and it's 95% likely the fuzzball I hold in my hand is red, what is the resulting probability that the fuzzball I hold in my hand is red?
Now, maybe you thought this didn't address your question, but actually, it did. It's almost precisely analogous to the question you asked.
You see, because verdicts are based on case details, the rate of accurate conviction is not an independent piece of information from the case details. In fact, once we know the case details, the rate of accurate conviction is almost entirely irrelevant: if we're using someone else's opinion (e.g. a jury's) to judge whether we think someone is guilty, it's only because we don't think we have the relevant information ourselves. The diagram for the situation would look like this:
case details -> jury's opinion -> our opinion
In such a situation, we're listening to the jury's opinion because we expect that it results from the case details.
However, if we know the case details ourselves, then knowing the jury's opinion won't tell us anything more about the defendant's guilt:
case details -> our opinion
We no longer need the jury as a proxy.
This phenomenon is called screening off. (Note that the entry linked to uses another example of the phenomenon from a different aspect of the Kercher case.) See the excellent Less Wrong post on the topic, Argument Screens Off Authority.
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