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This article reviews the formulation and evolution of the Philadelphia National Bank anticompetitive presumption through the lens of decision theory and Bayes Law. It explains how the economic theory, empirical evidence and experience are used to determine a presumption and how that presumption interacts with the reliability of relevant evidence to rationally set the appropriate burden of production and burden of persuasion to rebut the presumption. The article applies this reasoning to merger presumptions. It also sketches out a number of non-market share structural factors that might be used to supplement or replace the current legal and enforcement presumptions for mergers. It also discusses the potential for conflicting presumptions and how such conflicts might best be resolved.