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A peculiar principle of legal evidence in common law systems is that probative evidence may be excluded in order to increase the accuracy of fact-finding. A formal model is provided that rationalizes this principle. The key assumption is that the fact-finders (jurors) have a cognitive cost of processing evidence. Within this framework, the judge excludes evidence in order to incentivize the jury to focus on other, more probative evidence. Our analysis sheds light on two distinctive characteristics of this type of exclusionary rules. First, that broad exclusionary powers are delegated to the judge. Second, that exclusion on grounds of undue prejudice is peculiar to common law systems. Both features arise in our model.