Furthermore, we show that by setting a high barrier to discretionary control (e.g., by limiting access), Supreme Court justices can take advantage of appellate judges' desire to influence the law, thereby incentivizing appellate judges to increase informational effort: judges. act as screeners of those cases most likely to be of interest to the courts. See also Perry [1991] and Epstein and Knight [1998] for reviews of some of the empirical findings on which signals the Supreme Court appears to use. Furthermore, we show that higher opportunity costs on the part of judges generally imply a higher equilibrium threshold for a minority judge to write a dissenting opinion.
In Shavell's model, the error is of the misclassification type, while in Daughety and Reinganum's model, an appellate court determines error based on private information about what (he expects) the Supreme Court would do if it heard the case.
Model Set-Up
Thus, a judge who votes for cert represents (in our model) a coalition of at least four justices in the Supreme Court (i.e., we abstract from the coalition formation problem in cert voting). If the primary question is whether the lower court may be out of step with previous Supreme Court decisions (or the question is simply whether P or R actually wins), then uB = uSB > uSW = uW. Apfel, 1998, the Supreme Court majority supported limiting Congress's economic regulation, even though it was largely retroactive.
It was the fourth of these cases appealed to the Supreme Court and the only one where a certificate was granted (see Daughety and Reinganum, [1999]).
Payoff Functions for Supreme Court Justices and for Judge m
Conditional on a finding for P, justice expects to be in the majority with probability "Pi (thus predicting the highest possible utility, uB) and in the minority with probability 1 - "Pi (thus predicting the lowest possible utility, uW) ) . On the other hand, Justice i believes that with probability 1 - D(pM, b(pM, sm)) the Supreme Court will find R in favor if it were to review the case. Conditional on a finding for R, justice expects to be in the majority with probability "Ri (thus predicting the highest possible utility, uB) and in the minority with probability 1 - "Ri (and thus predicting the lowest possible utility, uW) ) .
Justice i, on the other hand, believes that with probability 1 - D(pM, b(pM, sm)) the Supreme Court would rule in favor of R if it decided to review the case. Depending on the finding for R, justice i expects to be in the majority with probability "Ri (and thus predicts the second highest possible utility, uSB, for the reasons explained above) and in the minority with probability 1 - "Ri (and thus predicts the second lowest possible applicability, uSW, again for the reasons explained above). Justice i is willing to vote to grant the certificate if and only if Bi(C, sAC) > Bi(NC, sAC).
Justice i is sympathetic to m's position on whether Vi(pM, pm) increases in pm. Justice i is not sympathetic to m's judgment about whether Vi(pM, pm) decreases in pm. Justice i can certainly be convinced if Vi(pM, 0) and Vi(pM, 1) have opposite signs.
Justice i tends to grant cert if Vi(pM, pm) > 0 for all pm and tends to deny cert if Vi(pM, pm) < 0 for all pm. For an unsympathetic and persuasive justice i, the function Vi(pM, pm) decreases in pm and justice i: . 1) will vote to grant certificate if a dissenting opinion pm0 [0, xi) reports; 2) will vote to refuse certificate if a dissenting opinion reports pm0 (xi, 1); and 3) is indifferent to pm = xi.
Equilibrium Analysis
Judge m would be willing to write an opinion for pm0 [xm, 1] if it would elicit certificate; moreover, justice I will vote to grant certificate upon receipt of such an opinion, because Vi(pM, pm) > 0 for all pm0 (xi, 1]. The arguments above generalize straight to the case from one to three sympathetic and persuasive judges (indexed) by i), again assuming that any remaining judges tend to deny certificate Type IIa Equilibrium: Judge m writes a dissenting opinion if and only if pm 0 [max{xm, xS}, 1] ; at least one judge votes to grant certificate upon receipt of such an opinion.
There are only two possible types of pure-strategy equilibrium for the case of one to three sympathetic and persuasive judges, assuming that any remaining judges are inclined to deny certificate; at least one pure-strategy equilibrium exists. Again, pM and pm are complementary in the sense that a higher value of pM increases the value for justice i to vote to grant certificate (recall that justice i is sympathetic). Justice m therefore now writes a dissent for pm0 [xm, 1] and justice i agrees to grant certificate if and only if a.
The above arguments generalize directly to the case of one to three disaffected and persuasive judges (indexed by i ), again assuming that all remaining judges are inclined to reject certification. Type IIb equilibrium: judge m writes a dissenting separate opinion if and only if pm 0 [xm, xU]; at least one judge votes to issue a certificate after receiving such an opinion. In Proposition 3 below, we summarize the conditions under which each type of equilibrium exists for the case of one disaffected and persuasive judge (the proof is in Appendix A).
There are only two possible types of purely strategic equilibria for the case of one disaffected and persuasive justice, assuming the remaining justices. However, since the disaffected judge i votes in favor of pm0 [0, xi], it remains true that judge i would be willing to vote in favor of the larger set [0, xi] of pm realizations if uB, uW , "Pi or " Ri were higher or if uSB, uSW or kSC were lower (and for the same reasons). Additionally, Judge m will be able to convince a favorable Judge i to vote to approve the certificate by writing a dissenting separate opinion for pm0 [xi, 1].
Type IIc equilibrium: Judge m writes a dissenting separate opinion if and only if pm 0 [xm, xU] c [max{xm, xS}, 1]; at least one judge votes to issue a certificate after receiving such an opinion.
Summary, Implications and Potential Extensions
If the Supreme Court consists of sympathetic justices, then the equilibrium subinterval for writing an opinion (this is a Type IIa equilibrium) is of the form [x,1], where x depends on the characteristics of the dissenting justice and sympathetic and persuasive justice(s). So if a judge's private information about the Supreme Court's probability of reversal is high enough (above x), he will write an opinion and cert will be granted. The Court of Appeals' opinion revealed a very high likelihood that the existing Supreme Court would want to reverse this case and change the law system-wide (change from maximum-resale-price-maintenance contract is a per se Sherman Act violation to apply a rule-justification test for assessment of possible antitrust cases similar to Khan).
When the persuasive Supreme Court justices are unsympathetic, the equilibrium subinterval for writing an opinion is within [0,1] (this was a Type IIb equilibrium). This dissent revealed a “mediocre” value of pm. The Supreme Court granted leave, but upheld the Court of Appeal's original decision by a margin of 7-2. Policy, Precedent, and Power: A Positive Theory of Supreme Court Decision Making,” Journal of Law, Economics, and Organization pp.
If all judges voted to reject the certificate based on the belief that no opinion came from the set [0, max{xm, xS}) c b, then judge m has an incentive to switch from not writing to writing by some pm0 b, since this will trigger cert (since maxi {Vi(pM, pm)} > 0 for pm0 b). On the other hand, if some judge voted to certify based on the belief that no opinion came from the set [0, max{xm, xS}) c b, then judge m has an incentive to deviate from writing to not writing for those values pmó [0, max{xm, xS}) c b. If right i were to vote to deny certification based on the belief that no opinion came from the set [0, xm) c (xi, 1] c b , then judge m has an incentive to switch from not writing to writing by some pm0 b because this will trigger cert (since Vi(pM, pm) > 0 for pm0 b).
On the other hand, if justice i were to vote to grant certiorari based on the belief that no opinion comes from the set [0, xm) c (xi, 1] c b ), then judge m has an incentive to go from writing to not writing for those values of pmó [0, xm) c (xi, 1] c b. If all judges were to vote to deny certificate based on the belief that no opinion came from the collection [0, xm) c (xU, 1] c b , then judge m has an incentive to violate for some pm0 b from not writing to writing since this will provoke certificate (since maxi {Vi(pM, pm )} > 0 for pm 0 b).On the other hand, if some justice will vote to grant certificate based on the belief that no opinion comes from the set [0, xm) c (xU, 1 ] c b, then judge m has an incentive to transgress from writing to not writing for those values of pmó [0 , xm) c (xU, 1] c b.
To see that there can be no other type of equilibrium (pure strategy), suppose that judge m does not write a dissenting opinion for a set of values pm [0, xm) c (xU, xS) plus some additional subsets of values b d [xm, xU] c [max{xm, xS}, 1] (excluding b = {xm}, b = {xU} and b = {max{xm, xS}}; see footnotes 26 and 29), and writes to the remaining values of pm. If all judges were to vote to deny the certificate based on the belief that no opinion came from the set [0, xm) c (xU, xS) c b, then judge m has an incentive to defect from not writing to writing for some pm0 b, since the year.
