In preparing for a course about alternative dispute resolution that I recently taught, I did some research into the relationship between probability theory and the way “decision analysis” (sometimes called “risk analysis”) is sometimes used to try to determine the “discounted settlement value” of civil cases. What I learned was unnerving. I share the products of that research here in the hope that neither defense counsel nor plaintiffs’ counsel will be lead by "decision analysis" into misevaluating their cases.
Why is “decision analysis” not a reliable tool for assessing settlement value? It’s not just because the results of decision analysis can be no better than the reliability of the estimates of each component of the formula. Nor is it just because the formulae that decision analysts use do not take into account so many factors that should play significant roles in settlement decisions, e.g., litigation transaction costs, the economic and other tolls of protracted uncertainty, or damage to reputation or relationships.
Rather, decision analysis cannot reliably determine the “discounted settlement value” of a case because the way it is used for this purpose violates fundamental assumptions in probability theory and pursues answers to kinds of question that triers of fact generally are not asked to address. An example will help illustrate these points.
Assume that there are two major contested issues in the liability phase of a tort case: causation and fault. A decision analyst might suggest that the likelihood that plaintiff would establish liability can be calculated by multiplying the likelihood that the plaintiff would prevail on the causation issue by the likelihood that she would prevail on the fault issue. Thus, if she had a 60 percent chance of prevailing on causation and a 60 percent chance of prevailing on fault, she would have only a 36 percent chance of establishing liability.
To determine the "discounted settlement value" of the case, our decision analyst would ask counsel to estimate the likelihood that the jury would award different possible levels of damages. Assume that counsel estimate that there is a 20 percent chance the jury would return an award of $200,000, a 60 percent chance of an award of $120,000, and a 20 percent chance of an award of only $50,000. Our decision analyst would suggest that to determine the probable magnitude of a damages award would be to multiply each of these possible damages figures by the separate probability that the jury would make that particular award, then to add the three resulting figures. The math in this part of this exercise would look like this:
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