Explaining the Justificatory Asymmetry between Statistical and Individualized Evidence

Abstract

In some cases, there appears to be an asymmetry in the evidential value of statistical and more individualized evidence. For example, while I may accept that Alex is guilty based on eyewitness testimony that is 80% likely to be accurate, it does not seem permissible to do so based on the fact that 80% of a group that Alex is a member of are guilty. In this paper I suggest that rather than reflecting a deep defect in statistical evidence, this asymmetry might arise from a general constraint on rational inquiry. Plausibly the degree of evidential support needed to justify taking a proposition to be true depends on the stakes of error. While relying on statistical evidence plausibly raises the stakes by introducing new kinds of risk to members of the reference class, paradigmatically 'individualized' evidence-evidence tracing back to A's voluntary behavior-can lower the stakes. The net result explains the apparent evidential asymmetry without positing a deep difference in the brute justificatory power of different types of evidence. The AsymmetryHere's a simple picture: something is evidence for p just if it raises the epistemic probability that p, and the strength of evidence-its power to justify epistemic actions like inference, belief, etc.-can be read directly off of these probabilities: e 1 is stronger evidence for p than e 2 iff the probability of p given e 1 is greater than the probability of p given e 2 . Let's call this simple-probabilism. This picture does not distinguish between statistical information and direct observation when thinking about their power to ground inferences. But sometimes there is an apparent asymmetry in their justificatory power; for example, consider two cases:(a) Prison Yard-a 1 -One hundred prisoners exercise in the prison yard. Ninety-five prisoners together assault a guard.Security footage reveals five prisoners standing against the wall refusing to participate, but is too grainy to identify them. The guard cannot identify his assailants. Alex is prosecuted for the assault, on the grounds that we know he was one of the prisoners in the yard, and therefore we can be 95% confident that he participated in the assault.(b) Prison Yard-b -One prisoner attacks a guard, and there's an eyewitness whom we know to be accurate under similar conditions 85% of the time. Alex is prosecuted on the grounds that the eyewitness testifies that Alex was the assailant.Let p be the proposition that ' Alex participated in the assault' . The following three judgments seem true:1. The evidence in the (a) case renders p more probable than the evidence in the (b) case.2. In the (a) case, our evidence does not suffice to establish p.3. In the (b) case, our evidence does suffice to establish p. This puzzling trio of judgments is an instance of the statistical evidence proof paradox. 2 Given simple-probabilism,