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Bar News - February 22, 2008

Using Decision Trees in Mediation



Decision trees are now being used more often in mediations as a way to value a case.  When used correctly, the primary benefit of a decision tree analysis is that it forces a lawyer to think carefully and systematically about his case.  However, as was first predicted by Marc Victor about 20 years ago (40 Bus. Law 617 (1984-85)), there is a tendency to simplify decision trees to the point that they lose most of this value.


To illustrate this point, consider a hypothetical patent infringement suit by Acme, Inc. against defendant Flywheel.  The suit alleges actual damages of $2 million and seeks treble damages for willful infringement, based, in part, on the hear-say existence of a memorandum of one of Flywheel’s engineers advocating just “copying” Acme’s invention.  As the law on what is “willful” is currently in flux, Acme’s success will depend on the court’s jury instructions.


The current tendency is to create a decision tree focusing on computations as follows:


The decision tree is then used to value the litigation at $2,660,000 by weighting each outcome by its probability:


                        .70 x .40 x $5,000,000    =       $1,400,000

                        .70 x .60 x $3,000,000    =       $1,260,000

                        .30 x 0                                =               0           



The quantitative result of this example may be somewhat helpful.  However, this decision tree does not produce the real benefit of full decision tree analysis, assisting, if not forcing, a lawyer to focus on specific details of a case.  Thus, a more detailed decision tree analysis of this hypothetical would not guess the likelihood of winning overall but focus on the probabilities of different outcomes on specific important issues. 


First, counsel should assign probabilities as to whether the court would find infringement.  Counsel, after listing the facts weighing “for” and “against” infringement, might assign a 90% probability of infringement.  Then counsel should ask whether the infringement is willful, which depends, in part, on the probability of finding the alleged memorandum.  Again, after listing the facts “for” and “against” finding the memo, counsel might assign a probability of 80% of finding the memorandum.  Finally, counsel might conclude that there is a 70% probability of a favorable jury instruction. 


This analysis results in the following decision tree.


Now counsel can easily determine the overall chance of success as follows:

                                                .90 x .80 x .70 = 50%

                                                .90 x .20 x .70 = 13%



Thus, there is a 63% probability overall of winning.


In the next step counsel can focus on the details of calculating the present value of any recovery.


First, probabilities are assigned to the chances of obtaining judgments in amounts of $1,000,000; $2,000,000; and $4,000,000.  Then probabilities are assigned to the length of time needed to collect on the judgment.  Then the present value of each judgment is calculated, at a discount rate of 6.0%, for the different times required to collect.

With these two decision trees, a bar graph showing a clear picture of the probability of  success in the litigation can be constructed.

The use of the full power of decision tree analysis allows counsel to understand better the strengths and weaknesses of his case and, thereby, both to plan his discovery more cost-effectively and to evaluate settlement options.  It also allows the client to understand better the basis for counsel's assessments and recommendations.


Paul C. Remus is an attorney with Devine Milliment & Branch in Manchester.  He has been a member of the NH Bar since 1978.

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