This section presents a simplified theoretical model by Priest and Klein (1984) based on divergent expectations and asymmetric stakes. Simplified because I have adapted the model by removing settlement costs related to a dispute.
A dispute is regarded as “not settled” if a verdict was rendered during trial in a court of law. All other cases that were terminated before trial by a judge or jury are regarded as
“settled”.
If a plaintiff thinks that they have suffered an injury due to a defendant’s action, they might bring the case to court. The amount of injury suffered by a plaintiff is denoted as J.
There are costs associated with initiating a court action in the form of a variety of legal expenses. Costs for the plaintiff are denoted by Cp and costs of the defendant is denoted as Cd. Before the suit goes to a court, the plaintiff will make a settlement offer. It is upon the defendant to accept or reject the offer. If a plaintiff’s threat is credible (as assumed by Priest and Klein) then the following equations should hold. A denotes the asking price of the plaintiff; and B denotes the offer or bidding price of the defendant.
A = Pp (J) – Cp
B = Pd (J) + Cd
Here Pp and Pd are the probabilities that the plaintiff or defendant will win respectively.
The condition at which negotiations fail and the case will proceed to court is if A > B.
Hence, based on the above equations, Pp – Pd > (Cp + Cd) / J. We see, therefore, that there are three factors that are behind non-settlement. Size of the stakes (J), legal and court expenses (Cp and Cd), and expected probabilities of the parties (Pp and Pd). The suit will move to court if the difference in expected probabilities of plaintiff and defendant (P) is greater than total court expenses for both parties (C) over size of total stakes (J).
Hence, P > C / J 4.2.1 Modelling expected probabilities
Over a period of time, the parties are well aware of their own court expenses and the size of the stakes. Uncertainty of the expected likelihood (probability) to win lingers though.
The authors have provided a sophisticated empirical model that shows the difference in the expected probabilities of prevailing between plaintiffs and defendants.
The model assumptions start with a decision standard known as Y*. This decision standard is based on the historical trends related to the court, jury and nature of dispute.
Both the plaintiff and defendant are aware of this decision standard (Y*) and make their own estimates (Y’) about their chances during trial (for a randomly selected case). Figure 8 shows the true decision standard Y’ for an individual case and a general decision standard Y*.
Figure 8 Probability distribution of a case. Source: Priest and Klein (1984)
The shaded part represents the chances of plaintiff winning the case. In this case the plaintiff may choose not to litigate because their own expectation lies to the left of the Y*
and hence away from the shaded area.
In real life both plaintiffs and defendants have some private information that determines the variations in their own estimates. If a random dispute makes its way to the court, below are the estimates formed by the parties:
Yp = Y’ + p
Yd = Y’ + d
p and d are independent random variables with zero expectation and identical standard errors.
Figure 9 shows the probability distribution around the plaintiff’s estimate for the individual dispute.
Figure 9 Probability distribution of a case with Plaintiff estimate. Source: Priest and Klein (1984)
Based on Figure 9, individual probability estimates of the two parties are drawn in Figure 10.
Figure 10 Individual probability estimates of both parties. Source: Priest and Klein (1984) At the core of Figure 10 is the shaded area (from the perspective of plaintiff). The expected probabilities of plaintiff and defendant lies far from the decision standard Y* in (a). The difference in “expectations” of the parties of a plaintiff victory is low in (a). This results in a higher likelihood of settlement. The difference is parties’ expectations of a plaintiff victory is high is (b). This results in non-settlement as the parties are likely to disagree on the outcome.
This constitutes the phenomenon of divergent expectations that results in non-settlement.
To summarize in a simple way:
“Where either the plaintiff or defendant has a ‘powerful’ case, settlement is more likely as the parties are less likely to disagree about the outcome of trial”
4.2.2 Accounting for asymmetric stakes
In the previous model, the total size of stakes (J) was held constant and equal for both parties. However, in real life situations, the resolution of a dispute may affect one party more than the other beyond the monetary amount of the judgement. For example, one party’s public reputation may be at stake.
The authors empirically show that when the stakes are inequivalent, non-settlement can occur even when the parties agree over the expected outcome of the trial. By using the earlier inequality of comparing the plaintiff’s asking price and the defendant’s offer / bidding price:
A – B = PpJp – PdJd – C
Jp refers the stakes of the plaintiff and Jd refers to the stakes of the defendant. If we assume J’ = (Jp + Jd)/2 and P’ = (Pp + Pd)/2;
The final inequality looks like below:
Pp – Pd > (C – S) / J’ + P’* J/J’
The interpretation of the above equation is such:
Litigation (or non-settlement) is more likely where the plaintiff has a small probability of winning and the defendant has a large probability of winning. This is contrary to the phenomenon of divergent expectations shown in the last section. An example scenario: if the stakes of the defendant are higher, relatively more disputes with a likely plaintiff verdict will be settled and relatively more disputes with likely defendant verdicts will be litigated. The effect will be the same if plaintiff has higher stakes and probabilities of winning are the other way around.