Good post though I’m not sure the whole discussion about MP and MT was necessary- isn’t the relationship between the break in and the murder biconditional (which I guess probabilistically speaking means that the specificity and sensitivity are about equally high)?
I think part of the problem we see is people either unfamiliar with or incapable of reasoning probabilistically. Yes the fundamental error the prosecutors are making applies to a deductive interpretation of their position- but my sense is the prosecutors (and probably most people involved) don’t realize that a convincing arguments for a guilty verdict could begin by showing that the probability of a staged break in was say, 1⁄3, independent of all the other evidence. Saying that doesn’t even sound like a point in favor of guilt. But of course 1⁄3 is well above a reasonable prior and requires a fair amount of evidence. And given enough additional evidence against Knox and Sollecito that estimate can go up to the .999 you want it at. But traditional rationality doesn’t give people a good way of thinking about how low-probability sub-hypotheses can provide evidence for high probability hypotheses.
Good post though I’m not sure the whole discussion about MP and MT was necessary- isn’t the relationship between the break in and the murder biconditional (which I guess probabilistically speaking means that the specificity and sensitivity are about equally high)?
I think part of the problem we see is people either unfamiliar with or incapable of reasoning probabilistically. Yes the fundamental error the prosecutors are making applies to a deductive interpretation of their position- but my sense is the prosecutors (and probably most people involved) don’t realize that a convincing arguments for a guilty verdict could begin by showing that the probability of a staged break in was say, 1⁄3, independent of all the other evidence. Saying that doesn’t even sound like a point in favor of guilt. But of course 1⁄3 is well above a reasonable prior and requires a fair amount of evidence. And given enough additional evidence against Knox and Sollecito that estimate can go up to the .999 you want it at. But traditional rationality doesn’t give people a good way of thinking about how low-probability sub-hypotheses can provide evidence for high probability hypotheses.