1 Reconciling asymmetric information and divergent expectations theories of litigation By Joel Waldfogel The Journal of Law and Economics, 1998 報告人：高培儒 2009/02/11

2 Abstract Two theories offer possible explanations of the litigation case that fail to settle, but their results differ from each other. The aim of this paper is to find the cause of difference, and reconcile it.

3 Abstract ： Divergent expectations Described by Priest, George, and Klein, Benjamin. ’’The Selection of Disputes for Litigation.’’ Journal of Legal Studies 1984 Jan Each party estimates case quality with error. Cases proceed to trial when, by chance, the plaintiff is more optimistic than the defendant.

4 Abstract ： Divergent expectations Cases far above and far below the decision standard generally settle. Only cases near the decision standard go to trial. So, as the fraction of cases adjudicated declines (T), this leads to a tendency toward 50 percent plaintiff win rate at trial (P), regardless of the fraction of plaintiff winners in the filed population.

5 Abstract ： Asymmetric information Described by Bebchuk, Lucian A. ‘’Litigation and Settlement under Imperfect Information’’ Rand Journal of Economics one party (informed) have more information about litigation than another (uninformed). Informed parties proceed to trial only when they expect to win. Hence, as the fraction of cases adjudicated declines (T), plaintiff win rates at trial (P) tends toward either 1 or 0, depending on the plaintiff is informed or uninformed respectively.

6 Abstract In this paper ： Waldfogel present evidence that the result for litigation is consistent with DE, not AI. However, he also found that AI is exist prior to trial. At the end of this paper, he reconcile this two theories and give an acceptable explanation.

7 I. The Two Models and Their Distinct Implication

8 A. Divergent expectations model Assume the standards exist for resolving disputes. Distribution of disputes, Y, is divided in to two parts at some particular value, Y*, and everyone know it. In the shaded part, to the right of Y*, the plaintiff win. In the unshaded part, to the left of Y*, the defendant win.

9 A. Divergent expectations model Assume that a particular dispute, Y’, is randomly drawn from the distribution of disputes like the above Figure. Nevertheless, two parties must estimate Y’ in order to predict the likelihood of the adjudication if they go into trial. and are assumed to be independent random variables with zero mean and identical standard error,.

10 A. Divergent expectations model The plaintiff estimates the probability of a plaintiff verdict,, is represented by the shaded area, so as defendant. Set the decision standard, Y*, at zero. >> >>

11 A. Divergent expectations model The plaintiff’s minimum settlement demand: The defendant’s maximum settlement offer: Where J is the expected adjudication award, Cp and Cd are respective litigation costs to the plaintiff and defendant, and Sp and Sd are respective settlement costs. Cases go into trial if Where C=Cp + Cd and S=Sp + Sd. This is to say that ‘’cases proceed to trial when, by chance, the plaintiff is more optimistic than the defendant’’.

12 A. Divergent expectations model

13 A. Divergent expectations model The greater the distance that Y’ les from the decision standard, the lower the difference is likely to be between the parties ‘ probability estimates of a plaintiff’s verdict. The figure above illustrates that those disputes with the Y’ far above or far below from the decision standard, Y*, are more likely to be settled than litigated. Because the majority of litigated disputes lie close to the decision standard, the proportion of plaintiff victories in litigated disputes will approach 50 percent.

14 A. Divergent expectations model In other words, when more and more disputes are settled (that is, the fraction of cases adjudicated T declines), plaintiff win rate at trial P will converge to 50 percent. This can be illustrated by figure below ：

15 B. Asymmetric Information model Assume that both plaintiff and defendant are risk- neutral. One of the parties to the dispute has some private information about factual issues that is relevant to estimating the expected outcome of a trial. Assume that the defendant is the party with private information in developing the model. It can be easily adjusted to apply to the case in which the plaintiff is the one with private information.

16 B. Asymmetric Information model If a dispute fail to settle, then it goes into a trial, and the expected litigation costs of the plaintiff and the defendant will be Cp and Cd, respectively. And, if the defendant lose the trial, the court will award a judgment W in favor of the plaintiff (which is denoted by J in DE model). On the basis of his information, the defendant estimates the likelihood of the plaintiff’s win in a trial to be ‘’p’’. The plaintiff doesn’t know the actual p, but he knows the distribution of p.

17 B. Asymmetric Information model And assume that the distribution of p, f(.), is positive in the interval (a,b), 0<a<b<1, and zero outside this interval. It will be assume that the litigation has a positive expected value for the plaintiff even if the actual p is the lowest value, that is, - Cp+aW>0.

18 B. Asymmetric Information model The game proceeds as follows ： 1.The plaintiff chooses a settlement amount and offers it to the defendant on a take-it-or-leave-it basis. 2.Then, the defendant decides whether to accept the offer. 3.If the defendant has turned down the plaintiff’s offer, the plaintiff will have to choose whether to litigate the case or drop it ； and since Cp+aW is assumed to be positive, the plaintiff will elect to litigate.

19 B. Asymmetric Information model First, consider the decision that the defendant will make if the plaintiff demands a settlement amount S. If the defendant reject, then he will expect to face a trial and the expected cost is Cd+pW. Thus the defendant will accept the settlement offer if and only if ： or Hence, the defendant will accept an offer S if and only if his type p is equal to or higher than q(S), where q(S) is defined by

20 B. Asymmetric Information model Now consider plaintiff’s decision. The plaintiff knows the probability of his offer will be accept is 1-F[q(S)] and be reject is F[q(S)]. If his offer is rejected, then, the plaintiff’s information now is improved. Plaintiff will know that the likelihood of winning will be Thus, the plaintiff’s expected profit will be

21 B. Asymmetric Information model Hence, the plaintiff will choose S to solve. Differentiating the equation, we can obtain the A’(S) is Let S* denote the solution to the plaintiff’s problem, and let q* denote q(S*). S* is characterized below ：

22 B. Asymmetric Information model The result above suggest that increasing in judgment award W increase the probability of trial (or we say the trial rate, T) and the plaintiff win rate (P). It also suggest that increasing in trial cost Cp and Cd decrease T and P. So, above all, in the AI model with a better-informed defendant, decreased T induced by decreased W (or increased C) cause P to approach zero.

23 II. Do the Data on the Relationship Between T and P favor AI or DE ？

24 II. Data favor AI or DE ？ Data include over 65,000 federal civil cases filed in the Southern District of New York (SDNY) between 1979 and 1986 and terminate by the end of 1989, and are drawn from Administrative Office (AO) of the U.S. Courts data set. Variables include whether the case is adjudicated or, if not then settled ； whether the case is decide for the plaintiff if adjudicated ； the procedural progress at termination ； and the size of the money judgment for the winning party. They are linked with the AO data by docket number. Next is the summary statistics by judge.

25 II. Data favor AI or DE ？

26 II. Data favor AI or DE ？ Data on the relationship between the adjudication rate (T) and the plaintiff win rate among adjudicated cases (P) can distinguish between the two theories. To do so, however, one needs prior information about the nature of the informational asymmetry in the case types examined. Three variables that may shed light on informational structure 1.the fraction of pro se plaintiffs 2.the tendency for litigation parties to be repeat players 3.the fractions of institutional, as opposed to individual parties

27 II. Data favor AI or DE ？ The hypothesis is that ： 1.Attorneys are better informed about likely case outcomes than plaintiffs themselves, so the fraction of pro se plaintiffs may be related to the quality of plaintiffs’ information. 2.A party participating in more suits will have better knowledge about likely case outcomes. 3.Institutions are better informed than individual.

28 II. Data favor AI or DE ？

29 II. Data favor AI or DE ？ The fraction of pro se plaintiffs ： very high for prisoner cases, high for civil right cases, intermediate for tort and labor cases zero for both contracts and intellectual property. We can expect plaintiffs in civil rights and prisoner cases to be ill informed relative to their defendants ； and we can expect plaintiffs in contracts and intellectual property cases to be better informed relative to their defendants ； labor and tort plaintiffs should be somewhere in between.

30 II. Data favor AI or DE ？ The plaintiff-defendant repeat play ratio are low at prisoner, tort, and civil rights cases. These are generally case types with one-shot plaintiffs suing repeat-player defendants. The fraction of parties that are institutions ： Tort, civil rights, and prisoner, are unbalanced. They have almost exclusively individual plaintiffs suing largely institutional defendants.

31 II. Data favor AI or DE ？ The data suggest that, tort, civil rights, and prisoner cases have relatively ill-informed plaintiffs. Waldfogel includes tort and civil rights cases, but excludes the prisoner cases for two reasons. First, very little money is at stake in prisoner cases. Second, plaintiffs in prisoner litigation typically have very low litigation costs. Nearly two-thirds of prisoner plaintiffs proceed without attorneys.

32 II. Data favor AI or DE ？ Testing between theories Data on litigation costs are not available. And, he observe the judgments awarded in the relatively small sample of adjudicated cases. So, in order to obtain a large number of judgment amounts per judge, he aggregate over all case types. Judgment award (J) are positively related with adjudication rate (T), which can be obtained from the figure below.

33 II. Data favor AI or DE ？ Then, he use weighted least-squares regressions (using the number overall and tort and civil rights cases per judge as weights) to test.

34 II. Data favor AI or DE ？

35 II. Data favor AI or DE ？ The positive relationship between adjudicated rate (T) and judgment size (J) are significant ； the similar result can be obtained by regressing tort and civil rights T on tort and civil rights J. This positive relationship is consistent with both AI and DE theories.

36 II. Data favor AI or DE ？ However, plaintiff win rate (P) in tort and civil rights also has relationship with J. So, he use instrumental variable, with J as an instrument for T, to test between P and T. The result shows a negative relationship between T and P and that as T approaches zero, P approaches roughly 40 percent. This is consistent with DE but not AI.

37 II. Data favor AI or DE ？ Why the data isn’t consistent with AI ？ One reason may be that actual civil litigation does not proceed like the basic AI theory. The bargaining environment of basic AI includes a take-it-or-leave-it offer by plaintiff that the defendant then either accepts or rejects.

38 II. Data favor AI or DE ？ In actual civil litigation, the process of settlement usually takes a long period of time. It is hard to believe that no additional offer occurs and that the plaintiff receives no additional information from defendant. For this reason, it may be mistaken to look to the relationship between T and P for evidence of Asymmetric Information in civil litigation.

39 III. Early Adjudications ： a reasonable test for AI

40 III. Early Adjudications The data of Administrative Office indicate the ‘’procedural progress’’ at termination, which allow us to determine how far a case has progressed. He aggregate the levels of procedural progress at termination into four rounds ： 1. before the plaintiff’s complaint is answered 2.after the plaintiff’s complaint is answered, but before the pretrial conference where discovery is scheduled 3.after the pretrial conference but before a trial begins 4.after a trial begins Next table shows the distribution of cases by their procedural progress at termination

41 III. Early Adjudications

42 III. Early Adjudications

43 III. Early Adjudications Suppose that shortly after filing the judge stands ready to adjudicate cases that (to the informed litigant and the judge) would have obvious outcome at trial. Figure below represents this idea

44 III. Early Adjudications All case with p b would be adjudicated early for plaintiffs. An uninformed plaintiff knows the distribution but does not know p for his/her case. An informed defendant knows the actual p.

45 III. Early Adjudications A better-informed defendant will accept plaintiff settlement offers in case with p>b and will reject when p<a, allowing the likely plaintiff loser to proceed to adjudication. Hence, with uninformed plaintiff and informed defendant, the testable implication of Asymmetric Information is a low plaintiff win rate among cases adjudicated early. On the other hand, with informed plaintiff and uninformed defendant, we can expect a high plaintiff win rate among cases adjudicated early.

46 IV. Settlement under Asymmetric Information gives Priest / Klein results

47 IV. Settlement under AI The selection of cases for trial is not properly characterized as one party’s response to the other party’s take-it-or-leave-it offer. Instead, the selection of cases for trial is a sequential process of settlements in the shadow of pretrial adjudication. Table 4 shows plaintiff win rates in cases adjudicated in the first round for each of six case types.

48 IV. Settlement under AI A striking feature of these win rates is that they are extreme, either close to zero or close to one. Early plaintiff win rates in tort, prisoner, and civil rights are close to zero. Early plaintiff win rates in contract, labor, intellectual property are close to one. These data are consistent with asymmetric information.

49 IV. Settlement under AI Assuming that second-round adjudication operates in the same manner as first-round adjudication. Plaintiff win rates should again be extreme, but less extreme than in the first round. This prediction also consistent with data in table 4.

50 IV. Settlement under AI The settlement hazard rates reach peak at third-round. It suggests that the discovery at third-round promotes settlement through transmitting information across parties. Settlement hazard rates for each round are computed as the number of cases settled in that round divided by the number of cases still active. And this is converted to a monthly rate by dividing the hazard rate for the round by average number of moths in the round.

51 IV. Settlement under AI Parties in the selected sample of cases going to trial have completed discovery. So, information should be less asymmetric in the cases going to trial. And, the process of pretrial adjudication and settlement has removed the cases with obvious outcome. Consequently, we can expect plaintiff win rates among cases going to trial to be less extreme and much closer to 50 percent than at earlier rounds. This is consistent with the figure below.

52 IV. Settlement under AI

53 V. Conclusion

54 V. Conclusion The evidence of asymmetric information in the litigation exist before trial. The process of actual pretrial adjudication and settlement, contrast to basic AI, which isn’t a take-it-or-leave-it offer, appears to eliminate both high- and low- quality cases. So, information is less asymmetric among the parties proceeding to trial than among the parties in all filed case.

55 V. Conclusion Consequently, the selection of cases for trial results in plaintiff win rates at trial approaching 50 percent. The pattern of settlement in each pretrial round appears to reflect AI. On the other hand, the pattern of cases proceeding trial appears to reflect DE.