Perhaps I have the proverbial cart before the horse... would a recusal come before a vote to grant certiorari? If so, and it’s a big if so, does the majority threshold remain at 4, even though there are now just 5 Justices voting? Or does the majority shift to 3?
Sorry for the delayed response.
The appellants are asking for Sotomayor and Kagan to recuse themselves from participating in the “cert conference” vote on granting the Petition for a Writ of Certiorari. The appellants’ rationale is that if Sotomayor and Kagan recuse, then the Rule of Four becomes the Rule of Three and only Alito, Scalia and Thomas will be needed to grant cert in Hollister v Soetoro.
I can find no historical basis for the number of justices participating in the cert conference being reduced to three.
My understanding is that four justices are required in order to grant cert, no matter how many recusals there are.
In any event, recusals at the Supreme Court are completely at the discretion of the individual Justice. There is no law that requires a Justice to recuse. However Elena Kagan has already recused herself from participating in oral arguments and decisions on any case that she had a hand in from when she was Solicitor General.
Finally, I am not aware of any published reports on who recuses from participating in Certiorari conferences.