Nash Equilibria in Litigation Settlement Negotiation in the U.S.A.

by supposedlyfun2 min read27th Mar 2021No comments

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World Optimization
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Epistemic status: Confident. Relevance: depends on how fast you think takeoff will be.

The overwhelming majority of legal disputes don't go to trial.  They either settle (66+% of cases, according to this article; up to 95% is the common wisdom) or get dismissed (some for lack of merit, some because the case settled but the parties' public filings just show that they dismissed all their claims against each other). 

So if you're a trial lawyer who wants to get optimal results for your clients, settlement negotiation is a much more important skill than trial presentation.[^1] And the keys to understanding how settlement works and why are all the typical tools of rationality.

[^1]: Provided that your opponent knows you can put on a good trial presentation if things get that far.  

Settlement Structure

 "Settlement" usually just means that 1) one side pays the other some money and 2) both sides give up, forever, any claims they have against the other and dismiss any pending lawsuits between them.

You might think that a better solution is for brilliant lawyers to swoop in and propose a seven-part swap involving a muskrat farm and Bitcoin futures that somehow maximizes both parties' outcome and leads their children to a dynastic marriage that will one day rule Sealand, but you'd be mostly wrong; in my experience, by the time people are suing each other, they never want to do business together again, and they are primed to be wary of uncertainty.  As observed in this post, contracts are all about risk apportionment, and if you think the other side is more likely than everyone else to breach (based on the evidence that they already did breach), the risk of doing business with them again isn't worth it even if you get every risk-apportionment clause you want, because it's expensive[^2] to enforce a contract even if your eventual win is guaranteed.

[^2]: The lowest estimate I would give a client for taking their extremely simple case to full trial, including all the necessary discovery, is $50,000.

Negotiation in Practice

When creative solutions are impractical, lawyers almost always negotiate by starting at extreme numbers (usually "plaintiff's best possible day in court", so a home run, and "defendant's best day," which is typically $0 but can also be a monetary judgment in the defendant's favor) and incrementing and decrementing:

  • Plaintiff: Our opening demand is $1,500,000.
    • Defendant: Our counter-offer is $0. The jury is going to think your client is a malingering liar.
  • Plaintiff: $1,500,000. You need to put some money on the table if you want us to negotiate for real.
    • Defendant: Fine. $10,000.
  • Plaintiff: $1,485,000.

And so on. Sometimes, the lawyers do the negotiating, so getting permission from the client before making each offer and conveying each counter to the client.  Usually, this means one offer per business day at best; lawyers and clients are busy. But some cases get done that way if the amounts aren't too large and/or the clients are both motivated to settle.

Other times, the parties hire a mediator, a professional dispute-resolver. They set aside a day, meet at neutral ground like the mediator's office, and pay the mediator ~$3,000 to do shuttle diplomacy, going back and forth between the two caucuses, conveying offers and discussing counters.  Mediators are almost always attorneys and are often retired judges (more on this later). Many, many courts nationwide require mediation before they will allow a case to go to trial--because it gets cases settled and clears up the courts' dockets. 

Game Theory!

I snuck it in already, before we even got to the Game Theory subhead. 

if you think the other side is more likely than everyone else to breach

Breaching = defecting! 

the risk of doing business with them again isn't worth it

Iterated games!

(based on the evidence that they already did breach)

Bayesian updates, too!  

Game theory and Bayesian reasoning under uncertainty also help us understand the whys of all of this goofily consistent negotiation drama: stepwise negotiation in general, the commentary associated with the offers, the amounts of the offers, the popularity of mediation. I hope to show that these are Nash equilibria and maybe-optimal solutions to common problems that arise in negotiation.

I'm going to stop here and break this down into multiple posts.  Next up: modeling litigation outcomes. Spoiler: Things get uncertain!

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