Courts as biased policy makers
Whether we like it or not, judges and tribunals have their own preferences and they often act as policy makers implementing their own preferences over outcomes. This section therefore considers the extreme case, where a judicial decision maker has their own preferences over outcomes and makes decisions based only on these preferences.
There are again two parties to a legal dispute: the plaintiff (P ) and the defendant (D), who do not know what the judge's true preferences are. Each party has to submit an outcome to the judge. A party wins the case if it is closest to the judge's true preferences, which are only revealed after the case is concluded. The judge's decision rule is very simple: he simply implements the outcome announced by the parties which is closest to his own true preference.
The rules of this game mean that the parties to the dispute will be influenced by their beliefs about the judge's true preferences, and will modify their positions accordingly. However, because the utility of the parties depends on the outcome, they will also take their own payoffs into account.
To illustrate what can occur, consider a simple example. Suppose that a judicial decision is simply a parameter J on the interval [ J, J]. This could be a policy outcome which has wider ramifications, or it could simply reflect the judge's own preferences about what is 'just' or 'fair' (or, indeed, efficient) in the particular case before him. The only role of the judge is to announce a decision J.
The game proceeds by each party simultaneously announcing a position on the interval [ J, J ], and then the judge chooses the position that is closest to his preferred position. The parties then receive payoffs when this announcement is made.
Assume that the parties are diametrically opposed to each other: the plaintiff's utility is increasing in J, and the defendant's utility is decreasing in J. Suppose that, as far as the parties are concerned, every judge is ex ante identical, with favourite policy J°. Neither party knows the true value of J°. Suppose that both parties have no information about the biases of the particular judge before them, so that, as far as they are concerned, and any value of J° is possible with equal probability. Hence parties' beliefs about J° are uniformly distributed on [J, J]. Since the plaintiff's utility is increasing in J, and the defendant's utility is decreasing in J, the plaintiff's most-preferred outcome is J°P = J , and the defendant's most-preferred outcome is JD = J. Finally, suppose that the parties are risk neutral.
Let JP and JD be the announcements that each party make. The judge awards the case to the party which is closest to his true preferences. The probability that the plaintiff P wins the dispute is:
where F(-) is the cumulative distribution function of each parties' belief.
x — J
If beliefs are uniformly distributed on [ J, J ], then F (x) = . Thus, the
plaintiff believes he will win with probability: J J
and the defendant believes he will win with probability:
Let the parties be risk neutral, and suppose that their benefit functions are BP (J) = J and BD (J) = - J. The winning party gets to implement their announced policy. Then the expected benefits are:
More concretely, suppose that [ J, J] = [0,1]. Then F j J + Jp |= J + Jp, and we get: ^
In the announcement game outlined above, in a Nash equilibrium, the first-order conditions are:
and so we get the unique Nash equilibrium:
The plaintiff and the defendant each announce their most favoured outcome, and there is therefore an equal probability that the judge will announce either outcome as his decision. If the judge's actual preference is J° > 1, then he will award the case to the plaintiff, whereas if
J° < 1 he will award the case to the defendant. The expected payoffs of
2 * Г 11 1 * 1 1
the parties are E [B*] = 1 -^ 1 = ^ and E [BD] = - 1- 1 = - .