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Decision and Risk Trees

Simply stated, Decision Tree Analysis is a quantitative way of looking at the consequences of decisions made under conditions of uncertainty.  It assigns a value – an “estimated monetary value”, generally abbreviated to “EMV” – to different decision paths. Its basic method is to apply the cumulative likelihood that something will happen to the anticipated net gains or costs if it does happen.  It’s built on the logic of discounting: if a 100% certain $100 is worth exactly that, then what is a 50% chance of winning $100 worth? In other words, what if I could win $100 in a coin toss, but only if the coin comes up heads?  The answer, of course, is $50, assuming no other cost, and no feelings of risk aversion or other values to consider. 

 

When more than one uncertain event will be involved, the method applies the most basic elements of probability theory: it multiplies the probability of each necessary event on the way to a specific outcome to arrive at its “cumulative probability.”   Considering the classic realm of coin tosses again: what if I am to toss two successive unweighted coins, but I will only collect that $100 if BOTH coins come up tails?  The cumulative chance of that happening is 25%. That’s because I have a 50% on the first toss, and then if I win the first toss, a 50% chance of succeeding on the second toss.  .50 x .50 = .25 or 25%.     Thus, the discounted value, known in the trade as the “Estimated Monetary Value, or “EMV”, of playing this little game is $25.  We reach $25 by multiplying the $100 payoff multiplied by the 25% likelihood of its happening.This logic can easily be applied to a litigation in which there are just a few or many layers of uncertainty.

 

While there is no legal mandate for litigants to settle at or near the discounted value of their case, it often serves as a guide for reasoned decision making about settlement.  This analysis also enables decision-makers to see each outcome considered possible, and to weigh that against the cumulative risk that it will occur.  For many clients, that matters more than the EMV, which is really a weighted average. They appreciate the exercise of thinking through: “How bad will it be if X happens? A the end of it all, what are the chances that Y will happen, and how would I handle it.” Of course, risk aversion, timing, and other circumstances factor in. Whether using the method primarily for the EMV, or for estimating the risk of various outcomes, these are familiar, logical ways things that people consider when making decisions.

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If you are unfamiliar with the method, and you’d like to have step-by-step grounding in the theory and the method, I am hereby shamelessly plugging the book that was the genesis of this website: Risk and Rigor: A Lawyer's Guide to Assessing Cases and Advising Clients (DRI Press 2019) [available on Amazon and also chapter by chapter as free downloadable pdfs]. The first few chapters walk you through the basics, in much the same way I teach it in the course, but with deeper and careful explanation of the reasoning and logic. The electronic version includes video inserts reflecting what I put on a black board or white board when teaching the material.  The second half of the book discusses more subtle and advanced use of decision trees for more complex cases.

 

On the other hand, if such things come easily to you, and a quick overview is fine, it may be enough to read some of the excellent articles posted on this website.

 

In my view, the visual aspect of the decision tree is important for client counseling.  The benefit is two-fold:

  • It forces more careful, thorough, deliberate thinking and discussion of what might happen – the possibilities, the likelihood - probabilities, and the consequences – outcomes and costs.  For example, WITHOUT using this method, when an attorney orally tells a client he or she has a “pretty good case,” what in the world does that mean – to the lawyer or to the client?

  • It facilitates clear and thorough communication and may reduce negative emotional impact, on the client or, at least, on the lawyer-client relationship.  When the attorney walks the client through a decision analysis in his case, it provides a constructive and shared logic and a framework for client decision-making.