When the law is contested and a case is appealed to a higher court, the higher court must, at a minimum, make two decisions. First, it must decide whether the lower court committed any legal errors (Decision #1), and if so, it must decide secondly whether any of those legal errors are serious enough to warrant a reversal of the lower court’s decision (Decision #2). Formally, let’s call Decision #1 (did the lower court make a legal error?) the choice between e and not e, and let’s call Decision #2 (if there is an error, is it serious enough for a reversal?) the choice between small e and large e. For ease of exposition, let’s limit our discussion to Decision #1, the choice between e and not e. (The same logic applies to the choice between small e and large e.) Under the traditional method of judicial voting (one-judge, one-vote), the votes of each judge are equally weighted. Thus the “one-judge, one-vote” rule can only tell us whether e is ahead of not e (or vice versa). By contrast, under bayesian voting, judges would have to disclose their degrees of belief in e or not e. As a result, bayesian voting generates more information than simple majority rule vote: a bayesian voting procedure would reveal the comparative intensities of the judges’ beliefs about e and not e.
Why would we want to know the relative intensities of the judges’ beliefs? Answer (in two words): fairness and accuracy. Let’s consider a non-legal example to see why bayesian voting based on degrees of belief is better than simple majority rule with equal weighting. (For this example, I thank Paul Tassi.) Specifically, imagine a population of TV viewers are asked to rank two TV series using bayesian voting and simple majority voting: Breaking Bad versus Mad Men (or Nurse Jackie versus Orange Is the New Black). Under majority voting, viewers could only vote for one show, even though both TV shows are very good. Under a bayesian voting method (such as Netflix’s five-star rating system), however, each viewer could express the intensity of his preferences. (In my case, for example, I loved Mad Men, but I thought Breaking Bad was the best TV show ever made.) In ethical terms, bayesian voting is more fair and more accurate than simple majority rule, for bayesian voting is not only more immune to strategic voting than simple majority rule; it also generates a more accurate picture of the voters’ relative preferences. In our next blog post, we will explain why we are calling our proposed method of judicial voting “bayesian voting” instead of “cardinal voting,” “range voting,” or “utilitarian voting.”