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TUTORIAL
ONE
DECISION
TREES FOR LAWYERS
By
Michael D. Freeborn
For our first tutorial, let's assume that your company has been sued in a 1-count complaint for
breach of contract, and the plaintiff is seeking $1 million. There is a
50-50 likelihood of winning the case, but if the company loses, you know that
the verdict will be $1 million. The company can settle the case by
paying the plaintiff's settlement demand, $600,000.
Should the company litigate or settle? (For the moment, disregard legal
fees.)
 Decision
analysis begins with an identification of the decisions which must be
made, the uncertainties which will influence the outcomes associated with
those decisions, and the values -- usually monetary -- which will attach to
those outcomes.
In our first example, the decision we must make is whether to litigate or
settle. If we choose to litigate, the outcome will be uncertain -- we do
not know for certain whether we will win or lose. (In contrast, we know
what the outcome will be if our decision is to settle -- the monetary value of
the settlement demand, or $600,000.
These elements of the "influence diagram" are typically represented by
a rectangle, oval and rounded rectangle, respectively. To see an
example, click on the graphic above, to the right. (Recognizing that many of
you will be viewing this tutorial with dial-up modems, we have elected to
expedite page loading times by using "thumbnails" of the graphics on
the text pages. After you have clicked on the desired image, just use
your browser buttons to toggle back and forth between text and the associated
graphic. Or, of course, you can print the graphics for future reference.)
Software programs are available which make it relatively easy to enter the
data in an influence diagram. The program used for the examples in this
tutorial is called "DPL" (an acronym for Decision Programming Language) by
Applied Decision Analysis in Menlo Park, California. Others which have
been used by the author include "Arborist" by Texas Instruments,
Inc., and "DATA: Decision Analysis by TreeAge Software,
Inc.
Regardless which program is used, they typically require the user to state at
the outset what "decision" must be made. Here, we would say
the decision is to Litigate or Settle.
 They
then typically ask the user to identify the "chance" events and
express a judgment about the probabilities associated with such events.
Here, we would say the uncertainty is whether we will win or lose the case if
our decision is to litigate. Here is how the DPL screen looks after we
have entered our opinion that there is a 50-50 likelihood of winning (or
losing) the case:
Finally, the program typically asks the user to specify the values of the
various outcomes. Here, we know that the case can be settled for
$600,000 and that if the case is tried and lost the verdict will be for $1
million. After entering these values in our influence diagram, the
program will construct a corresponding decision tree.
There is nothing magic about the mathematics involved. Indeed, it is
nothing more than arithmetic -- as we shall see in a moment. For a
simple example like this one, the entire process could easily be done with a
paper and pencil. However, the software becomes essential when there are
dozens of arithmetic calculations to be performed, and numerous
"branches" of a decision tree to be displayed.
 A
decision tree reflecting our analysis of this decision indicates that the
"expected cost" of litigating is $500,000.
This is the sum of several individual calculations.
For each potential outcome, we multiply the likelihood of that outcome (say,
.5, if there is a 50-50 chance of it occurring) by the actual monetary value
of that outcome (in this contract case, for example, we know that the outcome
will be either zero if we win, or minus $1 million if we lose.)
Thus, we know that the aggregate "expected cost" of a decision to
litigate is: (.5x0)+(.5x1,000,000)=$500,000.
In contrast, we know that the cost of settling is certain. It is
$600,000 because that is what the plaintiff tells us will be the precise
amount necessary to dispose of the case by settlement.
Here, good decision analysis suggests we should litigate rather than settle.
In doing so, of course, we are not guaranteed a better outcome than we could
have had by settlement. This brings up the question, what is a
"good" decision. There is a difference between a lucky outcome
and a good decision. One can make a "bad" decision and still
have a lucky outcome. Similarly, one can make a "good"
decision and still have an unlucky outcome.
Decision analysis will not improve your luck, but it will help you
understand the problem better and thus make better decisions over time.
Although a decision to litigate may still result in an unlucky outcome of a $1
million verdict, if the case were tried an infinite number of times, we know
that the average of the results would eventually approach the expected value
of $500,000.
Before going on to the increased complexity of Tutorial 2, let's take a quiz
to test our mastery of the concepts so far.
QUIZ: Assume all the same facts as above, except one -- we now
believe that there is only a 30% chance of winning at trial, rather than a 50-50 chance. Should we litigate
or settle under these circumstances? Obviously, this requires us to
compare the "expected cost" of litigating with the known cost of
settling, which remains $600,000. Is the expected cost of litigating:
(a) $300,000; (b) $600,000; (c) $700,000; or (d) $1 million?
ANSWER (select one):
(a) $300,000
(b) $600,000
(c) $700,000
(d) $1 million
Copyright © 2001 Michael D. Freeborn. All rights reserved.
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