The Judging Game

It is common to criticize judicial opinions for correlating all too obviously with a judge’s politics or for being 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. Getting to this conclusion requires us to set up the decision problem as it presents itself to the litigants (whether to settle) and as it presents itself to the judge (how to react to the selection effect) and to derive the equilibrium of their strategic interaction.

We call this the judging game.