The Judging Game

It is common to criticize judicial opinions for correlating all too obviously with a judge's politics, or to be as unpredictable as a coin toss. We argue that this is precisely what one should expect of a well-functioning legal system with rational, competent, mostly impartial judges. What is called the selection effect, namely the tendency for cases with a clear outcome to settle out of court, combined with a rational judge's accommodation of this fact, will under the right conditions, make a judge's decisions observationally indistinguishable from decisions based purely on political bias or a coin toss. To derive this conclusion requires us to set up the decision problem as it presents itself to the litigants (whether to settle or not) and as it presents itself to the judge (how to react to the selection effect). Once one does this, a paradox emerges, what we call the paradox of open methods: if rational judges decide to carefully evaluate the merits of the cases that go to court, they will soon come regret this as wasteful effort because the selection effect makes their final decision no different from one they would reach without paying attention to the merits. But if judges ignore the merits of the case, and this becomes generally known and taken into account by the litigants, judges will come to regret doing so because the selection effect will then cease to operate, and it will no longer be wasteful to pay attention to the merits of a case. This paradoxical seesaw can only be resolved in a full game-theoretical model of the strategic interaction between the judge and the litigants. We refer to this game as the Judging Game.