The Blue Bus Paradox is not about Statistics

Christian Ennsgraber

Universität Salzburg

In the Blue Bus hypothetical, a plaintiff is injured by an unidentified bus; the only evidence is that the defendant runs 80% of the buses on the route. This is widely taken to threaten formal-probabilistic models of legal fact-finding: a Bayesian who reads the civil standard of proof as P(liability|evidence) > 0.5 and admits market-share statistics as evidence appears committed to imposing liability where legal intuition denies it. Diagnoses range from rejecting Bayesianism outright (Allen and Pardo) to reformulating the standard of proof in comparative terms (Cheng). This paper argues that the choice between these positions has been miscast: the competing diagnoses are variants of an underlying “priors dispute” about which prior probabilities the law may admit.

The Blue Bus paradox is thus not a paradox about statistics, but about admissible priors. I defend a “constrained Bayesianism” on which priors must track “counterfactualizable” frequencies in L. Jonathan Cohen’s sense: a frequency is counterfactualizable if it tracks a stable causal disposition of the agent or system at issue, one that would persist across nearby possible worlds, rather than an accidental distribution. The Blue Bus market-share statistic fails this constraint: it records an accidental route distribution decoupled from the negligent conduct at issue. By contrast, an eyewitness’s reliability rate, DNA random-match probabilities, and the market-share distribution in the DES cases (Sindell) are counterfactualizable, because they track stable causal mechanisms. This account (i) explains the intuitive asymmetry between market-share and witness evidence, (ii) accommodates doctrines such as res ipsa loquitur, and (iii) justifies the high probative weight of DNA evidence. Finally, I argue that non-probabilist alternatives, such as modal anti-luck or normic support accounts, either fail to draw these asymmetries or implicitly presuppose the counterfactualizability constraint.

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