 In his purported counterexample, Blyth treats \(\r{B}\) and \(\neg\r{B}\) as indicating the two subpopulations (e.g., two different hospitals). Suppose that treatment \(\r{T}\) is positively associated with recovery \(\r{R}\) for each subpopulation. In that case, assuming equal odds, we would rather bet on the recovery of a patient in the treatment group (action \(g\)) than on the recovery on the patient in a control group (action \(f\))—regardless of whether that person is in group \(\r{B}\) or group \(\neg\r{B}\). Thus, since we prefer \(g\) to \(f\) in either subpopulation, and since all patients are either in group \(\r{B}\) or in group \(\neg\r{B}\), we can infer, by the Sure-Thing Principle, that \(g\) is preferable to \(f\) also when we don’t know whether a patient is in group \(\r{B}\) or group \(\neg\r{B}\). But this inference is mistaken if association reversal occurs: it is perfectly compatible with the above scenario that the overall frequency of recovery is higher for non-treated than for treated patients! Blyth (1972: 366) concludes that 