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Standards of proof


Civil Procedure | Evidence


The law speaks clearly on the standards of proof, but listeners often misunderstand its words. This article tries, with some common sense and a modicum of multivalent logic, to explain how the law expects its standards to be applied, and then to show how the law thereby avoids such complications as the conjunction paradox.

First, in accordance with belief function theory, the factfinder should start at zero belief. Given imperfect evidence, the factfinder will end up retaining a fair amount of uncommitted belief. As evidence comes in, though, the factfinder will form a belief in the truth of the disputed fact but also form a disbelief, or a belief in the fact’s falsity. At the close of evidence, the standard of proof requires only comparing belief and disbelief. For example, the civil standard, rather than asking whether a fact more likely than not happened according to traditional probability theory, asks whether the factfinder believes in the fact’s happening more than the factfinder believes that the fact did not happen. The burdened party need not push proof above 50% by dispelling the phantoms of every possibility, and the opponent need not generate a competing version of truth but can instead rely on denial to demand that the burdened party generate a belief.

Second, belief and disbelief being nonadditive partial truths, the mathematical result is that one cannot combine beliefs by traditional probability theory, as by using the product rule designed for conjunction of betting odds. Instead, one should use fuzzy logic, including its rule that conjoined likelihood equals the likelihood of the least likely element. Linking the elements in a chain tells a story that is as likely as its weakest link. Consequently, if each element of a claim or defense passes the standard of proof, the conjunction of elements will pass the standard of proof. The conjunction paradox thus vaporizes for factfinding, just as the law has always maintained. The law found the way to decide in accord with our best knowledge of the facts.