Building on Eric Posner and Adrian Vermeule’s valuable insights about the Bayesian nature of the judicial process (see their paper "The Votes of Other Judges"), I propose a simple method for improving judicial decision-making, a method I have previously christened "Bayesian voting" in honor of Frank Ramsey and Bruno de Finetti. Under this method of voting, judges would not only state the reasons for their decisions; they would also express their degrees of belief in their decisions by "scoring" the strength of the moving party's legal arguments, i.e. by assigning a numerical score reflecting their relative degrees of belief in what the proper outcome of an issue or case should be (depending on whether the judge is engaged in outcome-voting or issue-voting). By way of example, a judge’s degree of belief could be expressed in numerical terms anywhere in the range from 0 to 1 or some other uniform scale, such as 0 to 10. The higher the judge's score, the greater the judge’s degree of belief. A score below 0.5 would mean that the party with the burden of persuasion is not expected to prevail; a score above 0.5, by contrast, would indicate that the party is expected to prevail; while a score of 0.5 means the judge is undecided about which party should prevail.