Friday, March 26, 2010

Quantifying Uncertainty

One of the things that mediators sometimes do is to try to get parties to think about lawsuits as a series of probabilistic outcomes, i.e., what are the chances the case will get dismissed before trial, that the plaintiff will prevail before a jury, that there will be an appeal, that the defendant will file bankruptcy, etc.  Parties often need to make a conceptual leap before they can even begin thinking about their dispute in those terms, however.  A lawsuit does not start out as a game of chance.  It starts out as a story in which one or both  parties injured or betrayed the other, and both parties seek vindication and compensation for their respective grievances.  Clients approach a problem by telling a story and asking who is right and who is wrong, not by trying to examine the costs and risks of resolving their conflict by various means. 

Only after the parties accept the possibility that they assume some risk in presenting their story to the court, can you start talking about valuing the case in more mathematical terms.  So here I want to repeat some comments I made in another forum (started by John DeGroote) about the value of decision tree analysis in litigation. I think decision trees can be a useful tool in litigation and in mediation. Especially for people who like to try to quantify everything (and I admit to being one of those people). But there are two kinds of uncertainty that decision trees can never fully resolve. One is the "garbage in, garbage out" kind of uncertainty. When a lawyer says he has a 60% chance of prevailing on a claim, all that represents is a seat of the pants feeling about the case. That is not to say that the lawyer's assessment is wrong--it could be based on years of experience and some pretty good hunches about what juries might do with a case. But it is also not a very firm number to start with. And when you start with a very unscientific probability number as a basis for calculating the value of a case, you are conveying a degree of certainty about the ultimate value that is probably not warranted. Add in the uncertainties about things like appeals over issues that have not even materialized yet, and you are dealing with a whole lot of uncertainty.

The second kind of uncertainty you cannot eliminate is the uncertainty of predicting how people will deal with the choice between the mathematical probabilities of the decision tree analysis and the concrete offer on the table. So if you tell the plaintiff that they have the choice between the defendant's $50,000 offer and a 30% chance of scoring a million dollar verdict at trial (or you tell the defendant that they can either pay the plaintiff $500,000 or face a 30% chance that the plaintiff will get a million dollar judgment), you would think that taking your chances at trial would be the obviously better option in both cases, but a lot of people will take the inadequate offer rather than risk getting nothing (or pay the unreasonable demand even if they are very unlikely to lose at trial).  Notice in the above examples that we could be talking about the exact same case, only with different settlement offers.  And notice how that illustrates the wide variation in what a fair settlement might look like in that case.  (This analysis of course still works in cases where the plaintiff has a very high probability of prevailing.  The settlement price might just have to be somewhat higher to make the scenario plausible.)

Whether people choose to settle or not will often depend on how much they like to gamble and a lot of other psychological factors that cannot be very easily quantified. Remember how Monty Hall used to offer people the choice between something like $500 in an envelope or a one in three chance of winning a new car? A surprising number of people chose the envelope. Another example: What do you do when the weather report says there will be a 20% chance of rain tomorrow? Do you continue planning your picnic, or cancel it? Some people might keep planning an outdoor activity even if the weatherman says the chance of rain is 80%, but others will cancel if they see the smallest cloud in the sky.

Bottom line is that doing a decision tree exercise can be very useful, but mainly to demonstrate to people just how much uncertainty remains in front of them if they want to continue to litigate, and perhaps as a means of making people comfortable with the fairness of the settlement offer. That kind of analysis can't really give a precise indication of what a case is "worth," but it might help people decide if they want to settle or not.

(photo from


PaperChace said...

Nice post Joe. I must say that I agree with you for the most part. Decision trees are not precise. But decision trees do many things. They are an excellent tool for attorneys and mediators to help facilitate decision making. They help clients see that they can lose money in litigation.

In few of the cases where decision trees are employed does it matter how accurate a tree really is. I think the key is that it is sufficiently accurate to paint a picture of one party's view of a case. That's typically accurate enough for most people.

I responded more fully on the PaperChace decision tree blog at

Joe Markowitz said...

Thanks for your interest, PaperChace. You make an interesting point that the decision tree can highlight where each side's view of the case differs. But it's also interesting that even where, say, the plaintiff contends they have a 70% chance of prevailing at the next stage of the lawsuit, and the defendant contends that the plaintiff only has a 30% chance of prevailing, you can often still settle the case. Perhaps that shows that both sides pay some attention to the other side's assessment and don't totally credit their own, or that both those probabilities present enough risk that both sides would rather accept a more certain result.