The Journal of The DuPage County Bar Association

Back Issues > Vol. 20 (2007-08)

To Sue or Not To Sue: A Hypothetical Case Study in The Use of Decision Trees in Developing Litigation Strategy
by David M. Madden

You’re sitting at your favorite bistro idly chatting with your friend (and repeat client) Dino over a lunch of House Salad and Double-Fried Onion Rings with Cheese and Chili when he says, "By the way, [your nickname used by your most intimate friends], I’d like you to sue my dry cleaner for me." You think: "You’re kidding, right?" but you say: "Pray tell, how has this heinous villain damaged my dear and closest friend?"

Dino says: "You remember those platinum-and-diamond-covered leather pants I bought my wife for our 20th anniversary? I took them to DinDoit Dry Cleaners, and they totally wrecked the pants. The platinum has lost its sheen, the diamonds have no sparkle, and the leather feels, well, not leathery when you wear them." You refrain from asking Dino how he knows what his wife’s pants feel like when they are worn. Dino continues: "I paid $300,000 for those pants, and now they’re not worth $300."

You respond, delicately: "I’m certain that you, valued friend and client, would not have approached me with this case were it not worthy of prosecution before our highest state, federal, and international tribunals. Before we embark on our moral crusade against the defilement of opulent party-wear, however, let’s decide whether this lawsuit is worth the risk for you."

"What do you mean, ‘worth the risk’?" Dino demands.

"Let me explain," you respond.

About Decision Trees

One way to determine the best way to tackle Dino’s dilemma is to create a decision tree. A decision tree is a decision-making model that considers your options and the possible outcomes of anticipated events, and attempts to predict your best course of action. Skip ahead to Figure 1 for a moment for an example of a simple decision tree.

Decision trees can be a useful tool in helping to map out your best course of action, especially when you are faced with a wide array of decisions and possibilities.

Every decision tree has a starting point, or status quo, which represents your situation right now, before you have made any decisions and before any events have occurred which may alter your status quo. "Branches" extend from the starting point to "nodes." Each node represents either a decision which you can make (a "decision node"); an event with an uncertain outcome (an "uncertain event node"); or an ultimate result of the decisions you have made and the events which have occurred (a "result node").

Every decision node and uncertain outcome node has branches extending from it. Branches extending from decision nodes represent decisions you can make. Branches extending from uncertain outcome nodes represent the possible outcomes of events.

All branches extending from uncertain outcome nodes have percentages assigned to them. Each percentage represents the prob-ability of that outcome occurring, in relation to the other possible outcomes extending from the node. The percentages of all branches extending from an uncertain outcome node must add up to 100%, because the branches extending from that node must account for all possible outcomes.

Branches extending from decision nodes do not have prob-abilities assigned to them because there is no chance involved in a decision node—you control the outcome of your decisions.

All result nodes have values assigned to them. Values are deter-mined by taking the anticipated benefit of the result, subtracting the anticipated cost of reaching that result, and then multiplying that amount by the probability that the result will occur.

You assign percentages to uncertain outcome nodes and values to result nodes as estimates based upon your experience and understanding of the situation.

At the end of the process, your best course of action will be to make the decisions which lead to the set of result nodes with the highest collective value.

Now that we know what the parts of a decision tree are, let us put this theory into practice by growing a decision tree for Dino.

Dino’s First Tree

The status quo, or starting point, for Dino is that DinDoit Dry Cleaners has wrecked his wife’s pants, and Dino wants to do something about it. Initially, Dino has two options: (1) do not sue; or (2) sue. If Dino does not sue, he has a 100% chance of recovering $0. Then again, he will not have spent any money on attorneys’ fees or litigation costs.

On the other hand, you have determined that Dino would have a 60% chance of winning at trial and recovering the lost value of his wife’s pants of $299,700. You further estimate that it would cost Dino $90,000 in attorneys’ fees and other litigation expenses to try the case. So, if Dino sues, he will have a 40% chance of "losing" $90,000 in litigation expenses and getting nothing in return, but also a 60% chance of netting $209,700 if he wins.

A simple decision tree based upon these possibilities might look like Figure 1.

Let us break the decision tree down. First, why does the Not Sue "branch" state that the result will be a break-even at $0, rather than a loss of $299,700. If Dino does not sue, does he not lose all but $300 of value in the pants?

Yes, but Dino’s loss took place in the past. What is done is done. This decision tree is designed to help you make decisions going forward. Thus, the starting point on the decision tree assumes that the loss has already occurred, and attempts to analyze what the results of your decisions might be from the present, going forward.

Second, if we are not factoring the $299,700 loss into our decision tree, why are we factoring in the $90,000 in litigation costs? We include the $90,000 in litigation costs in our decision tree because they have not occurred yet. Whether these costs will occur will be the result of Dino’s decision to Sue or Not Sue. We cannot do anything about the $299,700 loss, but Dino can make a decision about whether or not to incur litigation costs. Accordingly, we should factor these costs into our decision tree analysis.

Third, why are the possible results of the Trial multiplied by the probability of that result occurring? For example, why is the 40% probability of Lose at Trial multiplied by the cost of the loss, -$90,000, for a "value" of -$36,000?

We multiply the anticipated result by the probability of that result occurring to give us an objective way to compare the value of possible outcomes. Without this step, a decision tree would not be very useful, because it would not provide us with any way to compare one possible result to another. Taking this step, however, allows us to "normalize" all results, and compare the "value" of a Win ($125,820) to the "value" (or "cost") of a Loss (-$36,000). In this case, it would seem that the normalized upside of a win is greater than the normalized downside of a loss.

Fourth, as a rule, all of the probabilities stemming from an "uncertain outcome node" must add up to 100%. In this decision tree, we refer to Trial as an "uncertain outcome node" because Dino does not control the outcome of this event—in other words, we cannot predict the outcome with absolute certainty. Based upon events which are not entirely within Dino’s control, he may either Win (60%) or Lose (40%) at Trial. For a moment, imagine that these probabilities do not add up to 100%, and that, instead, there is a 50% chance that Dino will Win and a 40% chance that he will Lose. That leaves a 10% chance of something else occurring. You have three options at this point. You can: (a) grow a new branch to account for the remaining 10% (perhaps settlement at a certain amount); (b) revise your existing probabilities to make up the difference; or (c) you can just leave the 10% un-accounted-for. I highly recommend choosing option (a) or (b), as option (c) will wreak havoc with your decision tree. Just trust me.

Finally, what decision should Dino make: Sue or Not Sue? The answer can be found by comparing the total value of each branch. The Not Sue branch has a total value of $0. The Sue branch has a total value of $89,820 ($125,820 for a Win minus $36,000 for a Loss).

Thus, the Sue branch has a greater value than the Not Sue branch, and the decision tree advises us that Sue is the more valuable option.

So, you should advise Dino to sue the dry cleaner, right? Not so fast.

Our decision tree grossly oversimplifies the situation. The tree set out in Figure 2 should provide a more complete picture.

Dino’s Second Tree

Figure 2 presents a more thorough analysis than Figure 1.

You still estimate that: (a) Dino has a 60% chance to win if the case goes to trial and a 40% chance of losing; and (b) Dino will incur $90,000 in attorneys’ fees and litigation costs to try the case.

Now, however, we have added the possibility that Dino and/or DinDoit Dry Cleaners will file a motion for summary judgment. You estimate that Dino will incur $30,000 in attorneys’ fees if one of the two parties files a motion for summary judgment, or $60,000 in fees if both of the parties file motions for summary judgment.

You undoubtedly noticed that the second decision tree has some other features which the first one lacked. First, you will notice some probabilities in parentheses. For example, let us say that Dino does Not File a Motion for Summary Judgment, but the defendant does (note your estimate that there is a 50% chance that the defendant will file a motion for summary judg-ment if Dino does not file one). Our tree tells us that there is a "10% (5%)" chance that Dino will Lose the whole case on Defendant’s Motion for Summary Judgment. What is with the "10% (5%)"?

Think of the two percentages in terms of two rules. In the following illustration, assume "Event A" represents the Defendant filing a motion for summary judgment and "Event B" represents Dino losing on the defendant’s motion for summary judgment. The first rule applies to the first probability (the 10%): If Event A occurs, there is a 10% chance that Event B will occur. The second rule applies to the second probability (the 5%): Assume that there is a 50% chance that Event A will occur and that there is a 10% chance that Event B will occur if Event A occurs. Therefore, multiplying the 50% by 10% results in a 5% overall chance that Event B will occur. Note that Event B will occur if and only if Event A occurs—that is Dino can only lose the defendant’s motion if the defendant, in fact, files that motion.

Second, you will also notice that Trial appears in the tree several times, with different values. If the case gets to trial, you have deter-mined that Dino will have a 60% chance to Win and a 40% chance to Lose. The value of each trial result changes depending on the path that the case takes to get to trial, however, because: (a) the costs are different (it will cost Dino more to go through cross-motions for summary judgment and then trial than it will if Dino just goes straight to trial without any motions for summary judgment); and (b) the probability of each event in your decision tree affects the ultimate probability of each result.

Finally, based on the new decision tree, what should Dino do? Again, we find the answer by calculating the values of each branch. The value of each branch is the sum of its results.

The value of the Not Sue branch is still $0: there is no cost and no risk to Dino, but also no reward. The total value of the Sue branch in the second tree has actually increased from our first tree, from $89,820 to $128,347. Remember, the total value of a branch—here the Sue branch—is computed by summing the in-dividual monetary values of each possible outcome on that branch. Accordingly, our tree still strongly favors Sue over Not Sue.

But, our analysis does not end there. Since we have determined that Sue is Dino’s best option, we can then determine whether Dino should File or Not File a motion for summary judgment. Based upon our analysis, the File branch has an ultimate value of $58,018, while the Not File branch has a greater value of $70,329. Accordingly, our decision tree advises us to Sue but Not File a motion for summary judgment.

Creating Your Own Decision Trees. Decision trees can be relatively simple to create. While Figure 2 might look somewhat complex at first blush, when you take it step-by-step it becomes straightforward.

When you are developing your next decision tree, use this simple process:

(1) Determine what the status quo is, which will be the starting point of your decision tree. For example, "My client has been sued."

(2) Determine what your realistic options are. These will be the first branches of your decision tree. For example, "We could do four things: (a) not respond to the lawsuit; (b) offer settlement; (c) file a motion to dismiss; or (d) answer the complaint." Create a branch for each of these options.

(3) For each branch, determine the next "node," whether it will be a result, a decision, or an uncertain outcome. For ex-ample, for your "not respond to the lawsuit" branch, the next node may be a certain result of a default judgment; or for the "offer settlement" branch, the next node may be an uncertain outcome, with the branches "plaintiff accepts settlement" and "plaintiff rejects settlement."

(4) Keep adding branches and nodes until every branch ends in a result.

(5) Now, follow each branch and fill in probabilities for each uncertain outcome and values for each result.

(6) Total up the value of each branch, compare the totals, and there you go!

Final Thoughts. While decision trees can be very useful, they are all about educated guesses—they are not a crystal ball, which will foretell the outcome of your case. You may develop a decision tree, which over-whelmingly predicts odds in your favor; yet, you may lose on a motion to dismiss. Or, your decision tree may inform you that your best decision is easily not to sue, but your client insists on pressing forward. What are your ethical obligations in that event?

Decision trees require that you have a reasonable basis for deter-mining the probability of an event occurring. If you are simply unable to assign a probability to an event, or if the probability you would use is just an arbitrary number picked out of thin air, then you are probably better off not using a decision tree. Assigning a random probability to an event will not be helpful, and will very likely lead to misleading results.

Decision trees are also based on generalities. Your decision tree could quickly become unmanag-eable if you attempted to map out every minute possibility in your case. You should consider "trim-ming" the nodes and branches of your tree to reflect only the most realistic possibilities and decisions. The risk, of course, is that you may trim away an event which will actually occur and will impact the structure of your tree.

For example, while Figure 2 may be a much more detailed diagram than Figure 1, even Figure 2 does not account for all of the possible choices and uncertainties. For example, it does not account for the possibilities of: (a) the defendant filing a motion to dismiss at the outset of the case; (b) the parties’ settling right away; (c) an appeal by either or both parties after trial; or (d) a motion for summary judgment being granted as to some but not all counts, among other things. What do you do with your tree when an unplanned event occurs?

Revise your tree. A decision tree is not something you create at the beginning of your case and just refer back to as the case progresses. You should revise your decision tree as each significant event in the case unfolds, using the status quo as your starting point. You should trim branches or grow new ones as old possibilities fall away and new ones become apparent, and reset probabilities and values.

Decision trees are not useful in every case. For example, an ex-perienced practitioner who encounters a relatively familiar fact pattern may not need a decision tree to be able to make an educated estimate regarding how the case will play out. At the opposite extreme, however, even experienced class action practitioners may find decision trees useful in mapping out litigation strategy in complex cases.

Decision trees can be useful far beyond determining whether to sue. They can be used by defendants in determining whether to offer settlement or gear up for trial; by businesspersons in deal-making; and by computer scientists in developing "artificial intelligence" algorithms. If you are really motivated, you can use a decision tree to assist you with just about any decision, such as what to eat for breakfast, or whether to buy a sports car.

If you are interested in learning more about decision trees or other decision-making models, there are numerous books and articles published on the topic. The simplest way to create a decision tree is the tried-and-true pencil and paper method. Alternatively, a number of computer programs can assist you with the task, such as Microsoft Word or a variety of more specialized decision-modeling applications.

Conclusion. As you and Dino wrap up your lunch-turned-strategy session, he tells you, "I agree with you wholeheartedly—let’s sue DinDoit, but hold off on summary judgment. I prefer my chances going straight to trial. Also, I’m so impressed with the thought you’ve put into my case, I’ll buy lunch."

Thanks to your decision tree, you have earned your client’s respect, and saved yourself fifteen dollars. Nice work, counselor.

David M. Madden is an associate attorney, focusing in commercial transactions and commercial litigation, Momkus McCluskey Monroe Marsh & Spyratos, LLC, in Downers Grove, Illinois.  He graduated from Michigan State University in 1998 with a B.A. in Political Science and Public Policy Studies and from DePaul University, in 2003 with a J.D. and Certificate in General Intellectual Property Law.

DCBA Brief