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10 November 2005

Experts and Trials I: Game Theory

John Friedman

No sooner had the recent posts on this blog by Jim Greiner about the use of statistics and expert witnesses in trials
(see here and here, as well as yesterday's' post) piqued my curiosity than I was empanelled on a jury for a 5-day medical malpractice trial. This gave me ample time to think through some of the issues of statistics and the law. I will spend my next posts discussing these issues from three different perspectives: the game-theoretic, the experiential, and the historical.

I first approach this problem from a game-theoretic framework. In Jim's second post, he spoke about how, in our adversarial legal system, an expert for one side tends to interpret the facts in the way most favorable for that side, without compromising her "academic integrity." He then listed several reasons why this might actually be best for the system. I tend to disagree on this final point; instead, I believe the adversarial nature of the system pushes us into a very bad situation.

To give my argument focus, we must first pin down the concept of "equilibrium." An equilibrium of a game is a strategy for each player such that, given the other players' strategies, the player is maximizing her return from the game. In this case, the game is relatively simple: Two parties to a lawsuit are the players, each with a set of expert testimonials interpreting the relevant statistics in the case (which makes up the strategy). We can represent the net message from the expert testimony for each side as a number on the real line: The more positive the number, the more pro-plaintiff the testimony.

We must make some simplifying assumptions to analyze this problem. Let us assume that the testimony for each side comprises two components: the "true opinion" and the "slant." When added together, "true opinion" + "slant" = testimony. (For simplicity, let us assume that these numbers are the actual impact of the testimony. Thus, if a testimony seems too biased and is discounted, the true number would not lie far from zero). In an ideal world, the court (either judge or jury) would survey the "true opinions" of many experts in the field; if enough opinions were positive, the case would go for the plaintiff. Economists often refer to such a case as the "first-best," the socially optimal outcome.

Many games do not yield the socially optimal outcome, though. Both parties can even be worse off playing the equilibrium strategies than if each played some other strategy, despite the fact that each party maximizes her payoff given the other players strategy. A classic example of such a situation is the "Prisoner's Dilemma." In my next post, I will explore how, in this legal setting, exactly this tragedy occurs.

Posted by James Greiner at 5:50 AM