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16 PerspectivesJanuary 4, 2009

Decision Tree Analysis in Litigation: The Basics

A sample Decision Tree, available in .pdf format here.

I remember my first mediation decision tree. It was late in the day, just before impasse, and our mediator was desperate to show my client and me that we had misvalued the case.  As he sketched it for us the approach made sense, but that was no time to pick up a new technique.  His effort ended no different than most attempts to learn about decision trees on the fly — with a confused client, a frustrated mediator and a lawyer about to change the subject.

Fifteen years later I know the value of a decision tree and, just as important, how to really use one — in connection with settlement discussions and as a part of an Early Case Assessment before settlement talks begin. Admittedly they take a little effort and some practice, but whether you’re a lawyer or a mediator or their client, you’ll see one soon. Knowing what a decision tree is and how to diagram yours will be worth the investment.

What Is a Decision Tree Anyway?

Often used in the business world, decision trees are “tree-shaped models of [a] decision to be made and the uncertainties it encompasses,” according to Dwight Golann in Mediating Legal Disputes. A decision tree “shows the various possible outcomes in a lawsuit and helps the parties evaluate the costs, risks and benefits of each outcome,” as Daniel Klein discusses more fully in his article Decision Trees & The Arboretum.

Stated simply, the decision tree is a tool used to value the multiple financial outcomes possible in any litigation — whether summary judgment is granted, the plaintiff “wins” a small amount, or something else happens.

Just as important, decision trees arrive at these values by translating the subjective judgment of trial counsel into monetary terms — as Patrick Lamb and Ron Friedmann and David Post have pointed out before, your trial lawyer’s interpretation of “a good chance of winning” might be very, very different from yours. A decision tree can eliminate this latent disconnect.

The Four Steps in Creating a Decision Tree

Kathleen M. Scanlon’s concise and helpful Mediator’s Deskbook, published by CPR, tells us that decision trees involve four steps:

  1. Listing the various possible events which might occur in the course of litigation (or beyond);
  2. Considering the costs or gains associated with each possibility;
  3. Discounting each possibility by its probability-estimated likelihood that it will occur; and
  4. Evaluating the overall picture by multiplying each possibility by its probability.

Make Decision Trees Work for You

You don’t need to wait until your next mediation to learn about decision tree analysis, because putting these four steps into action isn’t hard:

  • Identify Outcomes. Consider every outcome in your case that’s a realistic possibility — the plaintiff takes your initial Rule 68 offer, the court grants summary judgment, you lose because you can’t get that videotape into evidence, or whatever. Once you list everywhere the case could possibly go, sketch those outcomes on a “tree” similar to the one above, reproduced in a .pdf format (with additional explanation if you scroll to page two) here.
  • Consider the Costs of Each Possible Outcome. Once you know every path your case could realistically take, consider what it will cost to get down each path and what you’ll have to pay when you get there — and add those sums to your tree. Summary judgment may be the cheapest way out of the case for a defendant, but it’ll cost something (say, $40,000 in the example above) even if you win. It takes money to get to mediation, trial or appeal, and more money often changes hands once you’re there. Add these amounts together for each branch, and list them on the tree.
  • List the Chances That Each Possible Outcome Will Occur. Once you know everywhere you could go and how much it should cost to get there, you’ll need to apply a little judgment to determine the chances you’ll go down each route. You have a 10% chance of a “high” verdict of $500,000 if a plaintiff’s verdict comes in and it will cost $150,000 to get there? Write it down.
  • Do a Little Math. Ultimately you’ll add up the probability-adjusted values of all the branches on your decision tree to achieve the expected monetary value, or EMV, of your case. Simply calculate the value of each ultimate outcome, which is the cost of that particular result times the chances that it will occur, and add up all these figures to arrive at a final value.  In the example above with additional details appearing on page two of this link, its $124,000 EMV is nowhere near the $500,000 number the plaintiff may have focused on since he filed the case (shown above as $650,000 since the illustration includes attorneys’ fees), but it’s much higher than the $40,000 it will take the defendant to get through summary judgment, too.

The ability of decision trees to objectively highlight the real monetary value of the case, rather than the number each party may have focused on previously, is one of the key attributes of the tool, and I’ll write more about how to leverage that value here.

A Great — and Free — Tool to Try Decision Trees on Your Own

Dan Klein’s article Decision Trees & The Arboretum, mentioned above, is one of the best practical discussions of decision trees out there, and his website also has a free tool to compute simple decision trees called The Arboretum, where you can “create, save, and modify your own confidential decision trees”; he even has an express option where you can create a single tree without a login here. The decision tree at the top of this post was created using Dan’s online tool, and I’ll be pointing to it again soon.

By the way, that mediator who introduced me to my first decision tree had a point — a point that would have been better understood on mediation day if I had really known how to leverage decision trees in settlement discussions before I got there.

Try a decision tree in your next case. You’ll be glad you did.

[UPDATE:  For for more on Decision Tree Analysis, Settlement Perspectives' series on decision trees includes:

  1. Decision Tree Analysis in Litigation:  The Basics (this post);
  2. Why Should You Try a Decision Tree in Your Next Dispute?;
  3. Advanced Decision Tree Analysis in Litigation:  An Interview with Marc Victor, Part I;
  4. Advanced Decision Tree Analysis in Litigation:  An Interview With Marc Victor, Part II;
  5. Decision Trees in Mediation:  A Few Examples; and
  6. Avoiding the Limitations of Decision Trees:  A Few Tips from Mediators Who Use Them.]

    Categories: Decision Trees,Fundamentals,Mediation,Negotiation,Settlement

    16 Perspectives:

    michael websterSunday, January 11, 2009 8:44 pm

    A complex decision tree might help you find outcomes that you had not thought about, but it is highly unlikely that decision analysis is ever going to progress to give you an expected value of a case.

    The theoretical problem is with the assignment of probabilities and their meaning. Unless you are a just goofing around with numbers, the assignment of a probability to an event presupposes that there is a frequency of similar events to count. This is hardly ever true in litigation, unless restricted to something like employment dismissal cases. Even then, I have trouble interpreting the numbers as anything more than subjective probabilities, ie. just goofing around with numbers.

    Unfortunately, the website that you refer to does not allow the drawing of complex trees and has a very simple model, which I have a hard time believing is valuable.

    John DeGrooteSunday, January 11, 2009 9:15 pm

    Michael–

    Thank you for your thoughtful response. At the outset, it sounds like you have a need for a more robust decision tree product than the tool to referenced in my post on decision tree basics. Although I have not tried them, advanced decision tree products of which I am aware include those of Vanguard Software, available at http://www.vanguardsw.com/products/decision-tree-suite/, TreeAge Software, available at http://www.treeage.com/, and Palisade Corporation, available at http://palisade.com/.

    If others are aware of products that may assist with advanced decision tree needs, I would be interested in hearing about them.

    Thanks again for your comment–

    JD

    AshleyWednesday, January 14, 2009 7:03 pm

    Good article John.
    Hopefully this is just another step in the systematisation and commoditisation of legal services. There is software being used off-shore that uses the decision tree for matrimoniall settlement (Vic, Aus) and for managing employment disputes (UK). The latter has allowed the firm concerned to reduce its prices (by 50%).
    There is a real property software transactional process available locally that also uses decision tree architecture.
    The end result of all the above is the services supplied can be carried out by less qualified personnel, cheaper, in less time and faster – with a more certain outcome. It is good for clients and lawyers alike.

    michael websterWednesday, January 21, 2009 10:59 pm

    John;

    For 2 party litigation, the best decision tree software is gambit, an open source product. It will generate decision trees far faster than any of the commercial products.

    It has sophisticated equilibrium solving tools and methods – which are useful for comparing how changes to the payoff matrix effects the calculated solution.

    But, I would stress not the expected value of the game, and instead would focus on the completeness of the decision tree.

    The decision tree should help us mechanically span the entire strategy space, something that our ordinary intuitions will fail to grasp at first.

    John DeGrooteWednesday, January 21, 2009 11:18 pm

    Michael–

    Thank you for your comment. I haven’t had a chance to download it yet, but for those who may be interested I was able to find Gambit, the decision tree software you referenced, at http://gambit.sourceforge.net.

    Thanks again for your feedback–

    JD

    JacobTuesday, January 27, 2009 9:26 pm

    Michael,

    You raise a point often brought up by people when they first encounter decision trees. However, the notion that a person can magically enter numbers or “goof around” with a decision tree and get an expected value of a case diminishes the value of even a very basic analysis.

    Decision trees provide a great amount of value, and without rehashing the above post, some of that value is the defensibility and transparency in the attorney’s decision making process. As the post originally noted, its difficult in many contexts to say “Trust me, I’m the expert” but it is more acceptable to use a decision tree framework which gives some rational for making a decision.

    The value of decision trees also increases along with a tree-users experience. For example, it is likely that a person who is well versed with a certain field of litigation would have a more accurate estimate of the likelihood of prevailing in a case than a person who is not well versed in that field of litigation.

    Finally, as a producer of PaperChace litigation risk analysis software, I’d say that decision trees should be used as a guide and not as an absolute. Thus, when I teach decision tree analysis, or when I train users on our software, I encourage users to bracket their analysis using a best-case/worst-case framework. By conducting an analysis in this manner, we reduce the attachment of the attorneys/mediators and their clients to any one particular value. This often makes users more comfortable with decision analysis because there is a range of values that are “expected” and it reduces the perception of decision analysis as a type of crystal ball.

    John DeGrooteWednesday, January 28, 2009 7:18 am

    Jacob–

    Thank you for your thoughtful comments. You mention one thing that I want to reinforce — “[t]he value of decision trees also increases along with a tree-user’s experience.” Once I started using decision trees more regularly, I found that I could focus on my client and our analysis in the case at hand, rather than the intricacies of how to build the tree itself. Just another reason to do decision trees early and often . . ..

    Thanks again–

    JD

    Mediation Channel » A round-up of must-read articles for professional mediatorsWednesday, January 28, 2009 3:36 pm

    [...] strong case for using decision trees to improve settlement decisions in a two-part series.  “Decision Tree Analysis in Litigation: The Basics” introduces readers to decision trees –“tree-shaped models of [a] decision to be made [...]

    michael websterWednesday, February 4, 2009 9:08 pm

    Jacob;

    Thanks for your observations.

    I am very familiar with decision trees. My remarks about the probability estimates are grounded in measure theory: it is unlikely that legal cases are sufficiently close that we can assign them into equivalence classes.

    But, on the other hand, I accept your view that the use of decision trees and even ad hoc theoretically meaningless probability measures does force clients to climb down from unrealistic litigation expectations. And this is very valuable.

    (Still convinced that Gambit is the best 2 person litigation decision theory software out there, however!)

    Litigation Risk Links, Resources, and Information « Litigation RiskFriday, January 8, 2010 1:53 pm

    [...] John de Groote, a high profile mediator and blogger recently covered the topic of why mediators should use decision tree analysis in their next mediation in his post at Settlement Perspectives. [...]

    Myth 4: Decision Trees Have Not Been Widely Adopted by the Legal Community | The Decision Tree Analysis BlogFriday, January 15, 2010 1:16 am

    [...] Settlement Perspectives Series on Decision Tree Analysis in Litigation [...]

    Myth 3: Decision Trees are Difficult to Learn | The Decision Tree Analysis BlogSaturday, January 16, 2010 8:31 pm

    [...] a decision tree by hand and this a tutorial on decision trees is outside the scope of this post. John DeGroote has a great intro to decision tree analysis in mediation on his blog at Settlement [...]

    Top 5 Decision Tree Analysis Resources | The Decision Tree Analysis BlogSunday, January 17, 2010 8:11 pm

    [...] 1. Decision Tree Analysis in Litigation: The Basics [...]

    3 Settlement Techniques That Will Help Move A Case To Resolution – The Claims SPOTTuesday, May 25, 2010 11:32 pm

    [...] Decision Tree Analysis – If you have never worked with a decision tree I strongly recommend you try it. The process itself can be extensively debated, however, as another tool it’s is worth a try. The essential component to the “tree” is trying to place an empirical approach to evaluating and settling a claim. Decisions are raised, values are assigned and an outcome is determined.Once completed, a decision tree is a tool that can be shown to an opposing party to explain the basis for a position being taken. Many will argue the values and measures that you placed on the various “decision” points, but it is a technique that can remove the emotional aspect of a negotiation and demonstrate an objective approach to a decision.  You can learn more about using this approach in Decision Tree Analysis in Litigation: The Basics. [...]

    What a Proverb Can Teach us About Decision Tree Analysis and Mediation | PaperChaceFriday, October 15, 2010 11:35 am

    [...] Here is a description of a decision tree according to one of my favorite and often quoted mediators, John DeGroote: Stated simply, the decision tree is a tool used to value the multiple financial outcomes possible in any litigation — whether summary judgment is granted, the plaintiff “wins” a small amount, or something else happens. Decision Tree Analysis in Litigation: The Basics [...]

    5 Ways to Better Manage Internal Expectations in High Stakes Litigation | In-house AccessTuesday, March 20, 2012 4:41 pm

    [...] robust decision tree analysis of the value of the case, updated as appropriate, so you can recommend to stakeholders the best [...]

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    of John DeGroote.

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