American juries are asked to decide in criminal cases whether the state has proven its case beyond a reasonable doubt and in civil cases which side has the preponderance of evidence in its favor. I wonder how many Americans are really capable of making such sophisticated judgments. Do jurors more generally decide which side they "believe", as the two sides present their different narratives of the case at hand?
I spent years thinking in terms of Bayesian statistics -- how each piece of evidence changed the probabilities of one or another hypothesis. I am quite comfortable not "believing" either of two narratives explaining the same outcome. Indeed, I think it quite reasonable to assume that one might -- in principle if not in fact -- assign a probability that narrative A is true, a probability that narrative B is true, and a probability that neither narrative A nor narrative B is true.
I am also familiar in a general way with the literature on common cognitive biases I would guess I am more familiar the existence of such biases than the vast majority of Americans.
I have had some experience, documented in my doctoral dissertation, with the errors that experts make in estimating their own accuracy, and in statistical means for estimating accuracy of expert judgment.
I have also been involved in the review of many thousands of research proposals and fellowship applications, and have many times participated in decisions as to whether a review was or was not adequate, based on the background of the reviewers and observation of panel behavior.
I assume that the "preponderance of evidence" means that a jurist is to decide in favor of the narrative he/she thinks is more probable based on the evidence provided.
I an not sure how great a probability for the narrative provided by the state is required for a jurist to find that the defendant is guilty "beyond a reasonable doubt".
My basic point is that it does not seem necessary nor appropriate to "believe" one or the other narrative. It is possible and indeed preferable to consider the probability one would assign to each narrative to be true.