[jason1990]

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Firstly lets say that the jury originally believed that there was a 20% chance he was innocent. What precisely do I mean by that? It means that the jury thinks that if they were presented with a million identical cases with the exact same evidence, 200,000 of the defendents would be innocent. First make sure you understand that definition.

OK, now assume that the shoe size fits one percent of the population. Now lets go back to the million identical defendents. 800,000 are guilty. All 800,000 have that shoe size. 200,000 are innocent. 2,000 have that shoe size. The other 198,000 are sent home. The trial now is for 802,000 defendents. All identical with the (adjusted) exact same evidence. Now the jury believes that one quarter of one percent of the defendents are innocent. (2000 out of 802,000).

Bringing it down to one defendent, the shoe evidence should change the juries probability of innocence from 20% to one fourth of one percent.

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Consider the following hypothetical. Across the country, in another town, a second trial is happening at the same time. The second trial is identical to the first, with one exception. In the second trial, a witness on the stand casually mentions that the defendant wears a size 13 shoe. Neither jury at that time knows about the footprint, so the second jury does not consider this testimony to be relevant. Nonetheless, it is part of the transcript of the trial. Both juries then deliberate, and both conclude the defendant is 80% likely to be guilty.

Then comes the footprint, a size 13 footprint known to be the murderer's. The second jury already knows the defendant wears size 13. The first jury immediately checks his shoe size and finds it is 13. So both juries are now in the same situation and they should weigh this new evidence in the same fashion.

But watch what happens when the second jury performs your thought experiment. They consider a million identical cases with the exact same (pre-footprint) evidence. However, for the second jury, the evidence includes the fact that the defendant wears a size 13 shoe. So all 1 million of their hypothetical defendants wear a size 13. It follows that none of their hypothetical defendants are sent home after the footprint is discovered, and their 80% assessment does not change. What went wrong?