Computing The Probability of Gay Marriage in New York

Here is an interesting Combinatorics problem with an application to gay marriage:

Question: What's the probability of getting a favorable majority decision of four "Yes" votes from a panel of six judges?
Answer: Less than the probability of getting a favorable decision from a panel of seven judges.

This is a relevant question, since whether gay marriage will become legal in the state of New York depends on this outcome. According to this article in the Albany Times-Union, Court of Appeals Associate Judge Albert Rosenblatt has recused himself from hearing the oral arguments in the New York state marriage case Hernandez v. Robles on May 31. The highest court in New York State, is the 7-member Court of Appeals. Rosenblatt's recusal reduces the probability of a positive outcome (in favor of gay marriage) from a 50% likelihood (with a 7-judge panel) to a mere 11/32 chance (with a 6-judge panel). There's an equal likelihood of 11/32 of losing the case, and a 10/32 of having a tied result. If a tie occurs, the case is re-argued with a judge selected from a lower court. Of course, this assumes that each judge's decision is a random variable with equal probability of being in favor or against gay marriage.
Of course, no judge would make up their mind before hearing a case, would they?