## July 16, 2007

### Wall Street Journal law blog blooper on court size

The author of the Wall Street Journal law blog brought up an old hobby horse -- splitting the Ninth Circuit. Ashby Jones, reporting on some calculations (of dubious applicability) in a recent Los Angeles Times op-ed piece by law professor Brian Fitzpatrick, wrote that "as a court grows larger, it is increasingly likely to issue extreme decisions."

Larger courts are more likely to issue extreme rulings than smaller ones? This cannot be true in general. The effect that Professor Fitzpatrick identifies in his numerical example (which I won't describe here) is a subtle consequence of the finite size of the population (the judges) from which the three-judge panels that decide the appeals are drawn.  Let N be the size of the full court, and let s be the number of "extreme" judges. It should suffice to consider the probability of selecting three extreme judges at random. This probability is

s(s–1)(s–2) / N(N–1)(N–2).           (1)

As N grows larger (and s grows proportionately, as Fitzpatrick posits), the subtractions matter less and less. In the limit, the chance of an extreme panel is just (s/N)3. Contrary the the claim in the Journal's blog, this quantity is less -- not more -- than (1). The proof is left as an exercise to the reader.

--DHK