A Bayesian Solution to the Conflict of Narrowness and Precision in Direct Inference

The conflict of narrowness and precision in direct inference occurs if a body of evidence contains estimates for frequencies in a certain reference class and less precise estimates for frequencies in a narrower reference class. To develop a solution to this conflict, I draw on ideas developed by Paul Thorn and John Pollock. First, I argue that Kyburg and Teng’s solution to the conflict of narrowness and precision leads to unreasonable direct inference probabilities. I then show that Thorn’s recent solution to the conflict leads to unreasonable direct inference probabilities. Based on my analysis of Thorn’s approach, I propose a natural distribution for a Bayesian analysis of the data directly obtained from studying members of the narrowest reference class.