The most conservative court? Hardly

Boston Globe article "The most conservative court? Hardly" (October 10th, 2010) discusses the leanings of the Supreme Court over the last few years. What it lacks is the recognition that the average justice's opinion is not what makes up a court--it is the median Justice's opinion. Corrections offers a simulation of the median and mean of a court composed of 9 justices (though the number has changed, the spirit of the simulation remains). It is important to note that all that follows below is a simulation.

Presidents are elected every 4 years with a 50/50 split in expectation between parties. Each President picks up his party's preferences with a small deviation of his personal preference. If a Justice leaves, one is appointed with the current President's ideology plus a noise term. If a Justice does not leave, he changes his opinions slightly from last period in a random walk. Each Justice has a 5% chance of leaving in any given year.

Then for 9 seats from a simulated ~235 years, we can plot the ideology of the person sitting in that seat, depicted separately for each seat graphically below (click to enlarge).



Similarly, we can merge all the Justices into one graph, if it helps understand the magnitude of individual shifts (click to enlarge):



But what is important for the court is the median Justice, not the mean, and not any individual. We present the President's ideology along with the mean and median Justice ideology below (click to enlarge):



In the simple simulation above, for most reasonable parameter values, the median Justice, in part because the parties differ much more than the personality noise for Presidents and the ideology noise for their Justices. Indeed, in any number of most simulations we ran, the median variance was much greater than that of the mean. This is an important distinction that the Globe's discussion of individual Justices did not encompass (though its discussion of decisions remains relevant).