Congress is currently considering adopting a mathematical formula to assign shares in cancer causation to specific doses of radiation, for use in establishing liability and compensation awards. The proposed formula, if it were sound, would allow difficult problems in tort law and public policy to be resolved by reference to tabulated “probabilities of causation.” This article examines the statistical and conceptual bases for the proposed methodology. We find that the proposed formula is incorrect as an expression for “probability and causation,” that it implies hidden, debatable policy judgments in its treatment of factor interactions and uncertainties, and that it can not in general be quantified with sufficient precision to be useful. Three generic sources of statistical uncertainty are identified—sampling variability, population heterogeneity, and error propagation—that prevent accurate quantification of “assigned shares.” These uncertainties arise whenever aggregate epidemiological or risk data are used to draw causal inferences about i