How much bias is too much?

Prosecutors in the impeachment trial against Chief Justice Corona announced that the chief justice had favored Arroyo in 80% of the 31 cases involving the former president. While likely to be damning in the public eye, it's worth thinking about what those numbers actually mean. First of all, on average one would expect a the average unbiased judge to vote 50% in favor of any random plaintiff in a borderline case, so Corona voted 30% (80% - 50%) more often in favor of Arroyo than one might expect. The first question is whether that difference is meaningful, given that there were only 31 cases in the sample. The difference is large enough that it should be statistically significant, although one would also want to consider other factors that might account for the difference.



Moreover, of course judges are not unbiased, plaintiffs are not random, and not all legal claims are borderline. It's difficult to assess the numbers without a sense of the underlying merit of the cases. How many of those cases were split decisions in controversial cases, as opposed to unanimous opinions in rather mundane cases? Also, we would also have to compare Corona's voting pattern to other justices on the court. If the majority had a similar vote pattern, Corona wouldn't be such an exception.

Finally, if the prosecution is right and Corona favors Arroyo, why would he vote against her in 20% of cases? Again, we'd want to be sure that 20% is statistically significant, but it still must be explained. After all, if Corona was so loyal to Arroyo, why vote against her at all? It would be interesting to find out more about those cases.

In U.S. law, prosecutors are generally not allowed to use general statistical patterns as evidence. This announcement shows why. While Corona might have been unduly loyal to Arroyo, the headline oversimplifies the situation.

I have reposted the article below:

'CJ favored 80% of 31 cases involving GMA' By Jose Rodel Clapano (The Philippine Star) Updated February 24, 2012 12:00 AM Comments (1)  MANILA, Philippines - Chief Justice Renato Corona favored 80 percent of the 31 cases involving former President Gloria Macapagal-Arroyo in the Supreme Court (SC), a prosecutor said yesterday. On questioning of Senate President Pro-Tempore Jinggoy Estrada, Northern Samar Rep. Raul Daza said these are among the pieces of evidence that will show Corona betrayed public trust as stated in Article 7 of the impeachment complaint. “It turned out that there are 31 cases involving (former President) Arroyo,” he said. “Chief Justice Corona voted 80 percent in favor, more or less. 20 percent is not in favor.” Daza said the SC under the influence of Corona issued decisions very fast involving Arroyo’s cases. “Mabilis pa sa alas dose (Faster than 12 o’clock),” he said.