Wednesday, January 30, 2013

eDiscovery Economics: Part 1

In order to begin to meet the goals of this blog, I'm writing a multi-part blog article on eDiscovery economics.  I'll start with a broad view of the dynamics involved in legal conflicts, then drill down to the pieces that eDiscovery can impact.

The Model
More than 80% of state civil matters settle1 and more than 95% of federal civil matters settle2.  Looking at some of the economic models used for litigation can show what a huge impact electronic discovery can have in the dynamics and decision-making processes, such as whether to settle or go to trial.  One of the first models applied to litigation and legal conflicts first developed by W. Landes (1971)3 and J. Gould (1973)4 is known as the optimism model, given the name since it's based on the level of optimism, measured as a probability, that each party believes the have of winning (for the plaintiff) or losing (for the defendant).  These and many other models are described and examined in Tom Mecini's book5, The Economic Approach To Law, 2nd Edition.  Bear in mind this is only a model, so there are exceptions.  Also, it gets a little technical with a few formulas in the beginning, but I'll try to break everything down as I go.

In this model, the plaintiff's assessment of the probability that they will win a trial is Pp. The defendant's assessment of the probability that they will lose the trial is Pd. The plaintiff's and defendant's court costs are Cp and Cd, respectively. Let J be the monetary judgement amount that the plaintiff will recover if they win.  Here we assume there is no cost to settle.

The expected winnings for the plaintiff are the monetary judgement amount expected by the plaintiff (portion of the judgement as mitigated by the probability of winning) minus the cost of trial:
PpJ - Cp(1)

Similarly, the expected trial costs for the defendant are the monetary judgement amount expected by the defendant (portion of the full judgement as mitigated by the probability of losing) plus the cost of the trial:

PdJ + Cd(2)

Given the motivation to keep costs low, the plaintiff should be willing to settle for amount S if it is equal to or greater than the judgement minus the cost of trial,

S ≥ PpJ - Cp (3)

And the defendant should be willing to settle for any amount S, if it is equal to or less than the judgement plus the cost of the trial,

S ≤ PpJ + Cd (4)

So a settlement is possible if there exists an S, such that it is equal to or greater than what the plaintiff expects to win at trial, and less than or equal to what the defendant expects to spend on trial,

PpJ - Cp ≤ S ≤ PdJ + Cd (5)

or, equivalently,

PpJ - Cp ≤ PdJ + Cd(6)

which can also be written as,

(Pp - Pd)J ≤ Cp + Cd(7)

So the chance of settlement depends on, (a) the difference in perception between the plaintiff and defendant about their chances at trial, (b) the monetary judgement, J, and (c) the combined costs of trial.  From this inequality, the following can be observed:
  • As the stakes (judgement) increase, the chance for a settlement decreases
  • As the costs increase for either the plaintiff or defendant, the chance for a settlement increases
  • As the difference in perceived outcomes increases, the chance for a settlement decreases

Analysis Of The Model
To demonstrate the dynamics of this model, suppose a plaintiff is asking for a $50,000 judgement.  Both parties anticipate court costs of $10,000 and both parties believe they have an equal chance of winning at 50%.

The plaintiff should settle for any value greater than or equal to S = (0.5) $50,000  - $10,000 = $15,000.  The defendant should be willing to settle for any value less than or equal to S = (0.5) $50,000 + $10,000 = $35,000.  So any value between $15,000 and $35,000 should bring a settlement.

But suppose both parties believe they each have a good chance of winning at 80%.  For the plaintiff, the minimum settlement is: S = (0.8) $50,000 - $10,000 = $30,000.  For the defendant, the maximum settlement value is: S = (0.2) $50,000 + $10,000 = $20,000.  Since there does not exist a single S that can satisfy both conditions of being less than $20,000 and greater than $30,000, a settlement is not likely.

 Analysis Of Probability
So how do the changes in probability affect whether a matter settles or not?  We have to keep in mind that a settlement can be agreed on only if both parties are satisfied given the chances they believe they have of winning (plaintiff) or losing(defendant).

Let's take the same case and let the probabilities vary from 10% to 100% for both the plaintiff and the defendant.  The settlement lines represent (a) the minimum monetary value that the plaintiff is willing to accept, Sp, and (b) the maximum monetary that the defendant is willing to pay, Sd.  Figure 1 below shows the settlement lines where the defendant believes they have a 10% chance of losing and we are letting the plaintiff's probability of winning vary.

A settlement is possible for values in the shaded area that is below the Sd line and above the Sp line.  We can see that the the settlement lines cross at $15,000 when the plaintiff believes they have a 50% chance of winning and the defendant believes they have a 10% of losing.  So for those perceived probabilities, it's possible to get a settlement at $15,000 or less.

Figure 2 below shows the settlement lines where the defendant believes they have a 20% chance of losing and the plaintiff's perceived probabilities of winning are again varied.

Here, the defendant is less confident about winning and is willing to settle for a higher amount, $20,000 or less.

As expected, this trend continues - the settlement curves intersecting at higher and higher values - until the defendant believes their chances of losing is 60%.  Figure 3 below shows this scenario.

Here the defendant is not optimistic that they will win, so the settlement curves cross at a higher settlement value (since the defendant is more willing to settle) of $40,000, where the plaintiff is 100% sure.

After this point, for defendant probabilities greater than 60%, the settlement curves do not intersect.  So for this scenario,  assuming the costs and judgement do not change, a settlement could be reached for any value less than $40,000, the defendant's maximum, if the defendant's assessment of their chances of losing are greater than 60%, no matter what the plaintiff's perception of their chances of winning are.

The Effects of Cost 
Electronic discovery can have a huge effect on the costs for either the plaintiff and the defendant.  Taking a closer look at equation (3), we can see that if the defendant succeeds in getting a discovery request for a large, costly data set from the plaintiff, Cp will increase, thus decreasing the settlement, S, that the plaintiff will accept.  Therefore, the case becomes more likely to settle since the settlement value for the plaintiff has shifted down.

Likewise, if the plaintiff can increase the defendant's costs, Cd, through discovery, the matter again becomes more likely to settle, since the settlement value, S, in equation (4) has shifted up to become closer to the settlement value for the plaintiff.

The Effects Of Discovery
eDiscovery, and in fact any kind of discovery, has the "double-duty" effect of changing the probabilities for each party, moving them closer together as information is learned and shared between the parties, as well as affecting the cost, as discussed above.  How these changes affect the settlement lines and the possibility of settlement, can vary widely.
Next time we'll break down the eDiscovery process using the Electronic Discovery Reference Model (EDRM) to examine the costs and dynamics within each phase to discover how they can affect the outcome of a legal conflict, including how discovery can change the probabilities and costs as it progresses.



3. Landes, William.  An Economic Analysis Of The Courts, Journal Of Law And Econimics, 14: 61-107

4. Gould, John.  The Economics Of Legal Conflicts.  Journal Of Legal Studies, 2: 279-300

5. Miceli, Thomas J.  The Economic Approach To Law, Standford University Press, 2009.

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