Capítulo 5 Law and Economics

5.1 Empirical evaluation of law: The dream and the nightmare

(Donohue III 2015)

5.2 The Priest-Klein hypotheses: Proofs and generality

(Priest and Klein 1984) is very famous for the hypothesized “tendency toward 50 percent plaintiff victories”. (Lee and Klerman 2016) argues that the original paper is not very clear in a mathematical sense, so it demands a serious formalization. The main goal of this paper is to prove or disprove the P&K hypothesis using a tough mathematical formulation.

According to the authors, there are 6 hypotheses attributable to Priest and Klein:

  1. Disputes selected for litigation (as opposed to settlement) will not constitute a random sample nor a representative sample of all disputes.

  2. As the parties error diminishes and the litigation rates declines, the proportion of plaintiff victories approaches 50%.

  3. Regardless of legal standard, the plaintiff trial win rate exhibit “a strong bias toward fifty percent” as compared to the plaintiff trial win rate that would be observerd if every case went to trial.

  4. If the defendant would lose more from an adverse judgement than the plaintiff would gain, then the plaintiff will win less than fifty percent of the litigated cases. Conversely, if the plaintiff has more to gain, then the plaintiff will win more than fifty percent of the cases.

  5. The plaintiff trial win rate will be unrelated to the shape of the distribution of disputes. This hypothesis is about the plaintiff win rate in the limit as the parties become increasingly accurate in predicting trial outcomes.

  6. Because selection effects are strong, no inferences can be made about the law or legal decisionmakers from the plaintiff win rate. Rather, “the proportion of observerd plaintiff victores will tend to remains constant”.

The authors prove or disprove those hypothesis by using a mathematical formulation of the Priest and Klein setting. They use a particular one, but through this text i’ll reproduce their arguments using a similar version proposed on an unpublished (Gelbach 2016).

Almost every model for litigation starts with

  • \(Q_p\), the probability of plaintiff victory atributed by the plaintiff (possibly random).
  • \(Q_d\), the probability of plaintiff victory atributed by the defendant (possibly random).
  • \(c_p\), the cost of litigation for the plaintiff.
  • \(c_d\), the cost of litigation for the defendant (possibly null).
  • \(s_p\), the cost of pre-processual settlement for the plaintiff.
  • \(s_d\), the cost of pre-processual settlement for the defendant.
  • A joint probability distribution on \((Q_p, Q_d)\)
  • A bernoulli random variable \(\mathcal{L}\) indicating whether or not the ltigation ocurred.
  • A bernoulli random variable \(\mathcal{P}\) indicating whether or not the plaintiff won.
  • A litigation rule \(L(q_p, q_d) = \mathbb{E}[\mathcal{L}|Q_d = q_d, Q_p = q_p]\) that gives the probability of litigation given the parties subjective belief.
  • The probability of win of the plaintiff when the litigation occurred \(P(q_d, q_d) = \mathbb{E}[\mathcal{P}|\mathcal{L}=1, Q_d = q_d, Q_p = q_p]\)

Priest and Klein paper adds three parameters to the usual setting: \(J\), \(\alpha\) and \(Y\). \(Y\) is a random quantity that indicates the true quality of the case. If \(Y > y^*\), some threshold number, the plaintiff wins the case. \(J\) is the expected cost to the defendant if the plaintiff wins and \(J_p = \alpha J\) is the benefits for the plaintiff (if she wins). \(\alpha\) moderates the stakes. If \(\alpha = 1\), the stakes are symmetric.

Two important quantities for the selection of cases for litigation are

  1. Plaintiff’s expected win: \(q_pJ\alpha-c_p\)
  2. Defendant’s expected cost: \(q_dJ+c_d\)

Those quantities are important because (Priest and Klein 1984) states that " \(q_pJ\alpha-c_p+s_p > q_dJ+c_d-s_d\) is a sufficient condition for litigation“. The intuition behind this statement comes from the description of those quantitites:

  1. \(q_dJ+c_d-s_d\) is the largest amount the defendant is willing to pay, otherwise the cost of the settlement would exceed the expected payoff of the lawsuit.
  2. \(q_pJ\alpha-c_p+s_p\) is the lowest amount the defendant is willing to receive, otherwise the cost of the settlement would be lower than the expected payoff of the lawsuit.

(Lee and Klerman 2016) claims that (Priest and Klein 1984) uses this condition not only as sufficient but also as a necessary one, altough neither they explictly mention it nor i could find it explictly noted on the original paper. Through this text i’ll act as this is true.

Doing some algebra we get that

\[ \]

Under this model . Given \(q_p\) and \(q_d\), the expected gain of the plaintiff is given by \(q_pJ\alpha - c_p\) and the expected loss of the defendant is given by \(q_dJ + c_d\). So, there’s a settlement if and only if

\[q_pJ\alpha - c_p < s_d\] \[q_d J + c_d < s_c\]

generate a BibTeX database automatically for some R packages

Donohue III, John J. 2015. “Empirical Evaluation of Law: The Dream and the Nightmare.” American Law and Economics Review 17 (2). Oxford University Press: 313–60.

Priest, George L, and Benjamin Klein. 1984. “The Selection of Disputes for Litigation.” The Journal of Legal Studies 13 (1). JSTOR: 1–55.

Lee, Yoon-Ho Alex, and Daniel Klerman. 2016. “The Priest-Klein Hypotheses: Proofs and Generality.” International Review of Law and Economics 48. Elsevier: 59–76.

Gelbach, Jonah B. 2016. “The Reduced Form of Litigation Models and the Plaintiff’s Win Rate.” Research Paper, no. 16-22. University of Pennsylvania Law School.