I created the following graph after reading the Federal Circuit’s 3-2 claim construction reversal in Martek. Can you guess what the graph represents?
Mystery Solved by Joe Helmsen from Pepper Hamilton. Joe writes
“I think that the graphs represent the percent chance of having a majority decision in a particular direction given that each of x judges has a y% chance of deciding in that way. For example, the top line represents 1 judge at 90%, 2 judges have to go 2-0 (.9*.9=81%), 3 judges have to go 3-0 or 2-1 (.9^^3 + 3*.9*.9*.1 =97.2%, etc.).”
Right. One point of the graph is to illustrate the interesting phenomenon that the odds of convincing a “majority” are much higher when the panel has an odd number of judges. This is easy to understand when comparing a two-judge panel with a three-judge panel. A two-judge panel offers no room for error because requires that you convince both judges. On the other hand, a three-judge panel will side with you if you convince two of the three judges.
The graph also illustrates a second point – that in theory multiple judges tend to make marginal cases more predictable. Thus, an argument that will convince a judge 70% of the time would be predicted to carry the day in almost 90% of 12–member en banc panels.
Of course, this discussion relies on several false premises. Most notably, the analysis assumes that each panel member decision is independent of the decision made by other panel members. That is is clearly not true. Rather, the judges and clerks communicate and influence one another. In addition to independence, the analysis presented here presumes that each judge has the same likelihood of deciding the case in a particular direction.