The Difference between Blackstone-Like Error Ratios and Probabilistic Standards of Proof


  • Michael L. DeKay

    1. Michael L. DeKay is Health Services Research Specialist, Veterans Affairs Medical Center, Philadelphia, Pa.; Senior Fellow, Leonard Davis Institute for Health Economics, University of Pennsylvania; Post-Doctoral Fellow, Department of Operations and Information Management, The Wharton School, University of Pennsylvania.
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  • The author wishes to thank Ken Hammond, Reid Hastie, Gary McClelland, David Asch, Peter Ubel, and Terry Connolly for helpful discussions on these issues and for their insightful comments on an earlier version of this article. Correspondence concerning this article should be addressed to Michael L. DeKay, Section of General Internal Medicine (1 1lGM), Veterans Affiirs Medical Center, University & Woodland Aves., Philadelphia, PA 19104. Electronic mail may be sent via Internet to


Statements regarding the ratio of erroneous acquittals to erroneous convictions are often thought to have clear implications for standards of proof. For example, Blackstone's comment that “it is better that ten guilty persons escape, than that one innocent suffer’ is believed by many to imply a precise numerical value for proof beyond a reasonable doubt. Specifically, jurors should vote to convict only if they are at least 91 % certain of the defendant's guilt. Unfortunately, the belief that this decision threshold will lead to the desired ratio of judicial errors is simply incorrect. Depending on (a) the accuracy with which juries discriminate between truly innocent and truly guilty defendants and (b) the proportion of defendants who are truly guilty, this probabilistic standard of proof may lead to any ratio of judicial errors, including those favoring conviction of the innocent over acquittal of the guilty. Although standards of proof cannot be equated with error ratios in a simple manner, the problem lies not with probabilistic decision thresholds but with the desire to achieve a certain error ratio.