ECONOMIC THEORY OF SETTLEMENT AND CALCULATING SETTLEMENT AMOUNTS

 

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This introductory article explains the economic theory underlying settlement, setting forth why settlement is economically efficient, and the factors and calculation required to determine a beneficial settlement amount for each party.

 

ECONOMIC EFFICIENCY OF SETTLEMENT

Settlement is a mutually advantageous agreement that simultaneously reduces the risks faced by parties to litigation while also reducing legal costs. By settling, the defendant exchanges a large uncertain future liability for a smaller up-front expense, and the plaintiff exchanges a large uncertain future payment for a smaller guaranteed immediate payment. Both parties save money they would have been spent hiring attorneys to litigate the case. Due to the inherent efficiency settlement presents in not having to pay attorney to litigate, settlement a mutually agreeable settlement amount that serves both parties economic interest always exists. For this reason, a rational party will always have and amount, whether a floor in the case of the plaintiff, or ceiling in the case of the defendant, which they are willing to pay or accept, as the case may be, to settle the claim. As we will see, this amount is the weighted average current value of the future cash flows, discussed in detail below.

 

WEIGHTED-AVERAGE VALUE

A party will benefit by settling their claim for any amount better than the weighted average value of future cash flows adjusted for probability. Consequently, the weighted average value is the floor for the plaintiff and the ceiling for the defendant. Below I discuss the inputs required to calculate a basic weighted average value of a claim. As we will see, the weighted average value of future cash flows is not the same for the plaintiff and defendant.

 

Imagine you were selling a ticket that gave a 50% chance of losing $10, and 50% chance of winning $20, how much would you sell it for? The answer should be the weighted average value of the ticket, which is $5, as calculated below:

 

Weighted-Average Value

(probability of loss * cost of loss) + (probability of success * gain from success)

 

With numbers inputted

((.5) * (-$10)) + ((.5) * ($20)) = $5.

 

Similar to our ticket example, litigation has two outcomes, winning and losing. In additional to calculating the probability of each, you must also calculate the estimated award, and estimated cost of attorney’s fees for both parties through to trial. To reiterate, the five inputs are:

1. The probability of the plaintiff succeeding

2. The probability of the plaintiff failing (calculating by subtracting the probability of the plaintiff succeeding from 1)

3. Estimated award to plaintiff if they succeed

4. Estimated cost of attorney fees that will be incurred by plaintiff bringing the case through trial

5. Estimated cost of attorney fees incurred by the defendant defending the case through trial.

For a detailed article on how to estimate each of these factors, click here.

 

CALCULATING THE PLAINTIFFS SETTLEMENT FLOOR

Penny was crossing the street when she was hit by a truck driven recklessly by Dave. If Penny estimates that she stands a 65% chance of succeeding on her claim, that she will likely b awarded $100,000 in damages if she succeeds, and that she will incur $35,000 in attorney fees, we can calculate the weighted-average value of Penny’s claim as follows:

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Penny stands a 65% chance of taking home $65,000, and a 35% chance of losing $35,000. The weighted-average value of Penny’s claim is therefore $30,000, the sum of the probability adjusted values. This means that Penny would be economically benefitted by accepting any settlement amount greater than $30,000. The inverse is also true. Penny would be economically harmed by accepting any amount below $30,000, her settlement floor. If Penny is a rational plaintiff, she would refuse to consider any settlement amount that falls below her $30,000 settlement floor.

 

CALCULATING THE DEFENDANTS SETTLEMENT CEILING

Turning now to Dave. For the sake of simplicity, lets imagine Dave shares Penny’s estimates regarding the probability of her success, the likely amount that would be awarded, and he too estimates that he would incur $35,000 in legal fees defending the suit at trial. How much should Dave be willing to pay to settle the dispute? We calculate Dave’s weighted average below:

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Dave has a 35% chance of losing $35,000 and a 65% chance of losing $135,000, resulting in a weighted average value of negative $100,000. This $100,000 is Dave’s settlement ceiling. If Dave is a rational defendant, he will not consider any settlement requiring him to pay more than $100,000, as doing so would leave Dave economically harmed. Inversely, any settlement that requires Dave to pay less than $100,000 would be economically beneficial to Dave.

 

ENTER ZOPA

You might have noticed that there exists a $70,000 difference between Penny’s $30,000 settlement floor and Dave’s $100,000 settlement ceiling. This $70,000 represents a range of settlement values, each of which is acceptable to both parties. A settlement between $30,000 and $100,000 would economically benefit both Penny and Dave as it would be above the current value of the claim to each of them. In negotiation theory this range is referred to as the zone of possible agreement or “ZOPA.”

 

ZOPA SIMPLIFIED

Let’s talk sheep. Namely, a herder’s sale of a single sheep to a butcher. If the butcher is willing to pay a maximum of $15 to buy the sheep, and the herder is willing to accept as little as $5 to sell the sheep, then there is a $10 ZOPA that exists between $5 and $15. A sale of the sheep for between $5 and $15 will be economically beneficial to both the butcher and the herder, because the herder is getting more money than he would have accepted, and the butcher is paying less money than he had been willing to pay. Because the herder and butcher would each benefit from this transaction, we can expect a sale to occur for a price somewhere above $5 and below $15.

 

Now imagine a second scenario where the butcher is only willing to pay $5 for the sheep, and the herder is will on accept $15 or more. What we have here is the opposite of ZOPA, or what is referred to in negotiation theory as a negative bargaining zone or “NBZ.” In our example the NBZ is $10, representing a gap between the maximum amount offered and the minimum amount demanded. Where an NBZ exists, the transaction will not proceed to completion as doing so would economically harmful to one or more of the parties involved.

 

PENNY AND DAVE’S ZOPA

You might be thinking, yes, I understand how ZOPA came about in the case of the sheep, but where did the $70,000 ZOPA come from in the case of Penny and Dave? The $70,000 is the amount Penny and Dave cumulatively save by not having to pay their attorneys to litigate the case. You’ll remember that Penny and Dave each estimated that they would personally incur $35,000 in attorney’s fees at trial. By avoiding trial, they receive $70,000 in windfall savings available to be divided among the parties by negotiation of the final settlement amount.

 

The fact that the money saved on attorney’s fees becomes settlement ZOPA has important implications. First, where collective attorney’s fees are small, a smaller ZOPA exist and therefore settlement is less likely to occur. Inversely, where attorney’s fees are large, ZOPA expands, and there is an increased probability that a mutually agreeable settlement will be attained.

 

There are many examples of this theory playing out in practice. Imagine for instance the plaintiff that is being provided pro bono (free) legal services. That plaintiff’s settlement floor calculation will shift, the settlement floor will rise, displacing what would have been ZOPA, thereby decreasing the probability of settlement. Or in another example, imagine the large corporate defendant with underutilized in-house litigation counsel. Putting idle attorneys to work represents no additional cost, lowering the settlement ceiling, decreasing ZOPA, and again reducing the probability of settlement. It is for this reason that it is of the upmost importance that you estimate not only your own attorney fees but also those of your adversary. It may well be that your adversary’s cheap attorney is getting in the way of your settlement!

 

DOUBLE DUTY

There are at least two reason you want to calculate your adversaries’ floor or ceiling, as the case may be. First, the weighted average value of your adversary’s position will tell you their hard cutoff, the amount above or below which they cannot be expected to budge. Second, the gap between the plaintiff’s floor and the defendants ceiling, is the only amount actually being negotiated. A laser-like focus on this amount will pay off in spades. To illustrate the importance of calculating your adversary’s settlement position, note that in our example Penny calculated that any settlement in excess of her $30,000 settlement floor would be economic gain. But how much gain can she expect? By calculating Dave’s position, we saw that there was still another $70,000 of ZOPA above Penny’s $30,000 floor that she needed to be prepared to negotiate for. This $70,000 is fully 130% larger than the weighted-average value of Penny’s entire claim. This demonstrates the mistake of merely valuing your side of the equation. You need to know the size of the pie before you start negotiating for your piece of it. Remember, both parties benefit from settlement. The negotiation is over which party is going to get the larger piece of that benefit.

 

LET'S COMPLICATE THINGS A BIT

You might wonder why, if a $70,000 range of agreeable settlement values exists for a hypothetical $100,000 judgement, all cases don’t settle quickly. The answer is that we left some real world ZOPA shrinking effects out of our calculations. You might remember that in our example Penny and Dave each assumed Penny had a 65% chance of succeeding. This estimate was then used to calculate Penny’s floor and Dave’s ceiling. In the real world it will rarely be the case that adversaries will share the exact same estimate of the probability of the plaintiff succeeding. There are at least two reasons for this:

 

INFORMATION ASYMMETRY

In the real world, parties do not share identical information. One party will likely have more information than the other. This is particularly true in settlements that occur early in the litigation process, prior to discovery. Where parties have differing types and amounts of information, we can assume the they will also have differing estimates of the probability of the plaintiff succeeding. The effect of information asymmetry will be greatest early on, and in complex litigation that is heavily fact dependent. In run of the mill cases that hinge on few facts known to both parties we can expect information asymmetry and its effects to be minimized. Because information asymmetry is an unknown and unknowable factor, it is impossible to model it and adjust for its effect. Further, complicating its effect on settlement, information asymmetry can account for upward and downward adjustments to the plaintiff’s floor and the defendants ceiling depending on the information known to that party. To read a zopatopia article specifically addressing information asymmetry in settlement negotiation click here.

 

OVERCONFIDENCE BIAS

Second, and possibly more important than information asymmetry is human nature. Even where parties share identical information, they would still arrive at estimates that reliably diverge due to overconfidence bias. Overconfidence bias is the tendency for people to overestimate the likelihood of their success. If you doubt the existence of overconfidence bias just talk to anyone who plays the lottery, or consider the fact that 91% of Americans that were polled stated that they possessed above average driving skill, a fact dispelled by even a short trip on any road in the United States.

 

Returning to the realm of litigation, the pernicious effect of overconfidence bias is believed to account for the persistence of inefficient and enduring legal disputes. While the degree of overconfidence bias will vary from situation to situation, and person to person, we can safely assume it plays some meaningful role in most if not all settlement negotiations. As a result of their biases, we can assume Dave and Penny would actually have erred by overestimating their probability of success, with Penny overestimating the strength of her case, and Dave overestimating the strength of his defense. Maybe Dave would have reduced Penny’s chance of success to 50% when calculating his settlement ceiling, and Penny might have estimated her chance of success at 85% when calculating her settlement floor. These diverging estimates would have caused Penny’s settlement floor to rise from $30,000 to $50,000, and Dave’s settlement ceiling to drop from $100,000 to $85,000.

 

Given the wide disparity in estimates that can arise due to information asymmetry and overconfidence bias it may now appear that settlement may be more of a miracle than a foretold conclusion. But don’t forget the inherent efficiency of settlement, i.e. not paying attorney’s fees; which as we will see returns to save the day.

 

ATTORNEY FEES REVISITED

Thankfully for Dave and Penny, the $70,000 of inherent efficiency of settlement, which is the amount the parties collectively save on attorney fees by not proceeding to trial, now acts as a buffer, allowing the possibility for the possibility of mutually agreeable settlement despite overconfidence bias driving Dave’s settlement ceiling down, and Penny’s settlement floor up. The entire $70,000 of inherent settlement efficiency must be offset before an NPZ will form, foreclosing settlement.

 

In our initial example, where the parties shared the same estimate of the probability of Penny’s success, ZOPA was equal to the inherent efficiency of settlement, or $70,000. Now that Penny’s floor has increased to $50,000 and Dave’s ceiling lowered to $85,000, there exists only $35,000 of ZOPA, fully half the range of mutually agreeable values as where the parties shared a similar, objectively defensible, accurate estimate.
 

This demonstrates an important lesson. In real world settlements, ZOPA will almost always be less than the inherent efficiency of settlement. Put simply, we can expect the money saved by not litigating to be disregarded to some degree by the parties due to their reliable tendency to miscalculate the probability of their own success. In cases where the cost of attorney’s fees is high when compared to amount in dispute there will be a greater chance that these diverging estimates will not foreclose the possibility of settlement. In cases where attorney’s fees are relatively low compared to the amount in controversy, we can expect ZOPA to get eaten up quickly by diverging estimates of success, and in many cases an insurmountable NBZ will form.

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This article discussed the basic economics theory underlying settlement, including the fact that settlement is inherently economically efficient because it reduces the cost of attorneys fees borne by the parties. The article also set forth the five factors used to perform the weighted value calculation. We saw that where the parties share the same estimates of success, the amount of the cumulative attorneys fees created a range of mutually agreeable settlement values. We also saw that overconfidence bias reduced the plaintiffs settlement floor, the defendants settlement ceiling, and the ZOPA.

 

Now, by inputting your estimates for each of the five factors into the weighted-average calculation, and adjusting for the real-world biases discussed, you will arrive at the approximate amount of the plaintiff’s settlement floor, the defendant’s settlement ceiling, and the ZOPA over which you will be negotiating. To access zopatopia’s easy to use weighted-average value calculator click here.

 

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Sources

• Stevenson, Ola, “Are we all less risky and more skillful than our fellow drivers?” Acta Psychologica, Volume 47, Issue 2, February 1981, Pages 143-148

• Nalebuff, Barry “Credible pretrial negotiations,” Rand Journal of Economics 17 (Summer1987), 198-210

• Shavell, Stevens “Suite Settlement and Trial: A Theoretical Analyses Under Alternative Methods for the Allocation of Legal Costs,” Journal of Legal Studies 11 (Jan. 1982), 55-81

• Salop, Stevens C., and Lawrence J. White, “Economic Analysis of private Antitrust Litigation,” Georgetown Law Journal 74 (Apr. 1986), 1001-1064

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

• Gould, John P., “The Economics of Legal Conflicts,” Journal of Legal Studies, 2 (June 1973) 279-300

• Bebchuck, Luciana, A., “Litigation and Settlement under Imperfect Information,” Rand Journal of Economics 15 (Autumn 1984), ,404-415 1984

• Thompson, Leigh; Loewenstein, George "Egocentric interpretations of fairness and interpersonal conflict" Organizational Behavior and Human Decision Processes (Mar. 1992) 176-197