Independent scholar David Post (via the Volokh Conspiracy) recently brought the following “wild voting paradox” to our attention. In general, appeals at the federal level are decided by a panel consisting of three judges. Now, let’s imagine a case involving two legal issues on appeal, such as standing and immunity. Let’s say judges A and B believe that the original plaintiff has “standing” (i.e. may bring an action against the defendant), while judges B and C think that the original defendant is not immune from legal liability as a matter of law. In other words, only one judge–Judge B–thinks the plaintiff has standing and that the defendant is not immune from liability, so the defendant should win this hypothetical case on appeal, right? Not so fast … The “wild voting paradox” here is that the final outcome in this case depends on which voting rule (or “voting protocol”) the judges use to decide this case. If the judges adopt an “outcome voting” rule, for example, then the defendant will win the appeal, but if the judges follow an “issue voting” rule instead, then the plaintiff will win because one coalition of two judges believes that the plaintiff has standing while another coalition of two judges believes that the defendant does not have immunity from liability.
To the above analysis, we would only add the following point: this voting paradox may be intractable (i.e. insoluble) because any attempt to solve the paradox through a procedural vote would itself potentially be subject to the same paradox. Why? Because a procedural vote on which voting rule to adopt (i.e. “outcome voting” or “issue voting”?) itself consists of two separate issues: (1a) should the panel agree to take a binding procedural vote on which voting protocol to use or (1b) should the panel allow each judge to decide for himself which voting rule to follow?, and if the former option is chosen, (2) which voting protocol should the panel adopt? In any case, if you find this voting paradox as fascinating and intractable as we do, you may want to check out a recent federal appeals case Hanover 3201 Realty v. Village Supermarkets illustrating the paradox here (via the CA3 blog) as well as this comment thread about the Hanover case here (via reddit).
Pingback: Bayesian Voting (Part I) | prior probability