Mediation Math -- The Power of Combinations

by Andrew Flake

As mediators, we often find ourselves at the intersection of complex disputes and seemingly irreconcilable positions. But what if I told you that one of the keys to unlocking creative settlements lies in a simple middle school math concept – combinations? Both of my children were studying for school finals last week, so I admit that math was on my mind, but bear with me.

Let’s start with a fundamental: the parties’ interests as distinct form their positions.

In a breach of contract case, for example, the plaintiff’s legal position might be that the defendant breached a contract governed by the UCC, entitling it to consequential damages. But the plaintiff’s true interests could span its reputation, its customer relationships, ensuring an upcoming product launch takes place, and more. Likewise, the manufacturer’s interests may extend beyond just payment – securing future business, exploring new product lines, and maintaining market standing.

In mediation, understanding the parties’ underlying interests – more even than the formal claims and legal positions – can be crucial for reaching mutually satisfactory outcomes and thus settlement. In fact, here’s where the mediation math comes into play. Once we’ve identified a set of party interests, we take those interests and begin generating options to address them.

As I now know from my kids’ preparation for math finals, the formula for combinations is C(n,r) = n! / (r! * (n-r)!), where “n” is the number in your set, and “r” is the number of ways you combine them. In our example, suppose we have six options – three interests of the customer, and three of the defendant manufacturer. Since that a settlement proposal could incorporate any number of these, up to all six, the combination formula yields a pretty surprising 63 unique combinations! That’s 63 potential settlement agreements, and thus 63 different ways to resolve the matter, an exponential increase in potential solutions.

Compare that with relying on essentially one option, whether or not one party pays the other, and how much. We don’t have to be probability professionals to recognize that when we add to the money conversation dozens of additional interest-based settlement options, we’ve dramatically increased our chances of success.

And the great news is that getting there does not require using the combination formula, or doing any math at all! You need only think through the parties’ interest-based options. Coming up with even a handful will substantially improve your odds, though the more options you generate, the more possibilities you have, almost exponentially.

Yes, it will require some additional preparation, and some dedicated thinking time, but as Albert Einstein observed, and I find this hold more true in litigation than most areas, “the significant problems we face cannot be solved at the same level of thinking we were at when we created them.”

With 10 types of fruit on this mediation table, these mediating parties have at least 252 healthy snack combinations!

So the next time you find yourself at the mediation table, or even better, in your pre-mediation planning, work to think beyond just the pleadings and the parties’ legal positions. Think through and engage with their interests, and then list as many options as you can for how to satisfy them. In short, remember the power of combinations; if you do, you’ll give yourself, and your mediator, a tremendous head start in getting to settlement.

P.S. If you’re just interested in the concept of combinations, using a combination calculator will give you a feel for how they work. If you’re not a math person, my apologies for the formula: At least I didn’t share my calculations or ask you to check my work! 🙂

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