There are many constitutionally permissible formulations of the reasonable doubt jury instructions. Am. Jur. 2nd Trial § 1159. None contain language encouraging the jury to escape the cognitive biases that attend the evaluation of low probabilities. For example, Prospect Theory suggests that people tend to “neglect or underweight outcomes that occur with very small probabilities. Cf. here Suppose that the sum total of the evidence presented to an ordinary juror at trial suggest a 1% probability that the defendant is actually innocent of the alleged crime. (Putting aside, for the moment, questions of whether an exact probability like 1% can be properly represented; presumably, cognitive representations of probabilities are fuzzier than that.) The juror will tend to discount this probability to a negligible amount, perhaps zero. To the juror, the probability that the defendant is innocent will “feel like” zero, even though if the juror had to put a number on it, she would call it a 1% probability. A juror in this position would convict. Of course, this violates what most people would want the reasonable doubt standard to do: at least for serious crimes, we would be very uncomfortable knowing that one of every hundred people jailed was innocent. According to prospect theory, and the studies that confirm it, all low probabilities are downgraded. Assume that the jurors in any given trial construct some probability of innocence based on the evidence and that these probabilities, while subjectively determined, are not random but nevertheless vary around a mean. In cases where the probability of innocence is low, jurors will systematically underweight these probabilities downward. To the extent that subjective determinations of the probability of innocence go into jurors’ decisions of whether or not to vote for acquittal, the cognitive tendency to underweight low probabilities will cause more jurors to vote for guilty than is justified by _their own_ subjective weighting of the evidence.