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Louis Kaplow, Optimal Proof Burdens, Deterrence, and the Chilling of Desirable Behavior, 101 Am. Econ. Rev. 277 (2011).

Abstract: The optimal stringency of the burden of proof is characterized in a model in which relaxing the proof burden enhances deterrence but also chills desirable behavior. The results are strikingly different from those in prior work that uses a simpler model in which individuals only choose whether to commit a harmful act (so only deterrence is at stake). Moreover, the qualitative differences between the optimal rule and the familiar preponderance of the evidence rule----and related rules that look to Bayesian posteriors----are great, much more so than revealed by prior work.