Adding It All Up: Psychology and the Law

Two of Sally Clark’s children tragically died in their cribs. At Ms. Clark’s murder trial, Roy Meadows testified that the chance of cot death was one in 8,543. He then opined that the chances of it happening twice was one in 73 million. Ms. Clark was found guilty. Only after an extraordinary appeal supported by the Royal Statistical Society was it acknowledged that Mr. Meadows’ math was wrong. Meadows’ one in 73 million figure was derived by multiplying the likelihood of one cot death by itself. This calculation is only accurate when there are two random and independent events. Mr. Meadows ignored that some risk factors (i.e., genetic abnormalities, environment) made it impossible to assume. A book discussing the Clark trial is appropriately named How Numbers Get Used and Abused in the Courtroom.

Studies show that parties frequently over-value their cases. There are many reasons: over-confident lawyers, stubborn clients, and an attorney-client communication dynamic that often encourages lawyers and clients to sugarcoat their recommendations. Another explanation is people often avoid probabilistic evaluations and rely on cognitive biases known as heuristics.

On Let’s Make a Deal, Monty Hall showed a contestant three doors. Two of the doors concealed goats and the other a car. Monty would ask you to choose a door. Then Monty would always reveal a goat behind one of the two remaining doors. Afterward, Monty asked you whether you would like to switch. Numerous studies show that 90 percent of people reject the offer to switch. However, switching doubles your chances of winning the car.

If your reaction is that switching cannot be advantageous, you are not alone. The Monty Hall problem has confounded people for years. In 1990, when Marilyn Vos Savant noted in Parade Magazine that switching was advantageous, thousands of people – including prominent mathematicians – insisted that she was wrong. Studies of why the Monty Hall problem is so hard help to illustrate how cognitive biases impede our ability to assess risk.

Why switch? There was a one in three chance that the car was behind your selected door. Under the game’s rules, in both situations where your original selection was one of the goats, after Monty reveals the other goat – and he has to - the car must be behind the unselected door. In other words, if the player switches, she will win every time she initially selected a goat. Thus, in two out of three scenarios, you will win the car when you switch. Switching doubles the likelihood of winning.

Conditional probability is more complicated than it seems. People allow the equiprobability bias to convince themselves that once only two doors and two outcomes remain, they have a 50-50 chance. Studies show people strongly believe in the correctness of decisions made under the equiprobability bias, which explains the letters to Parade Magazine. Bayes Theorem is used to calculate conditional probability. I am not saying that lawyers need to know it to settle cases, but they should strive to make assessments without succumbing to cognitive biases.

If most people think there is no difference between staying and switching, why does virtually everyone stay with their door? Why not switch if it does not matter? Something else, other than lousy math, is going on.

The Monty Hall game is challenging because multiple cognitive illusions lead players to stick with their initial choice. People are more upset when they take an affirmative act that leads to a poor result than had their passivity led to the same result (the status quo bias). Moreover, once they select a door, it becomes more valuable to them, illustrating the endowment effect. If a second person is asked whether they want to switch doors, they do so at a much higher rate because the selected door was not their door.

One study shows that the older we get, the harder the Monty Hall game is (i.e., grade-schoolers switch more than high schoolers, etc.). Another shows humans are more resistant to learning the advantage of switching than pigeons! Our minds get in the way. Despite being intelligent and diligent, lawyers are human and susceptible to the errors that beset all of us.

The good news is that the techniques for figuring out the Monty Hall game generally apply to case evaluations:

(1) Make sure you verify all your assumptions (by adding more doors, most people realize the benefits of switching);

(2) Look at the problem from the other side’s point of view (don’t focus on the door you selected; what information was learned about the other doors?); and

(3) Reframe the problem (people asked to consider the frequency of events often view things differently than when they think of probabilities).

Lawyers are asked to look into the future when assessing the value of a case. The ultimate result of the case depends on how various factors impact others – i.e., will the court allow broad discovery, how will key witnesses perform, what will the jury instructions look like, will experts be allowed to testify, and will the court find certain cases persuasive. It is the job of a lawyer to assess each of these factors and strategize accordingly. It only makes sense also to take steps to ensure that cognitive biases are not impeding your efforts to quantify them accurately.