Supreme Equal Justice, A Fool-Fight at the Court

Since both the Democrats and the Republicans think that their antithetical Supreme Court justice, respectively Thomas or Kagan, should recuse their self from the case; I am surprised that neither side has made the obvious recommendation. I suppose that neither side tends to think reasonably or logically, or at all for that matter; but really isn't it self-evident what should be done?

Maybe they could go on that "Do You Think You're Smarter" show and get inputs from some adolescents on how to handle this riddle: How do you get a rational and fair hearing without the potentially biased justices participation? This is truly a thorny conundrum. It would probably take the wisdom of a Solomon or an Oliver Wendell Homes jr. to find their way through this thicket. Of course it could be that it is really, really simple. That simplicity doesn’t prevent it from being beyond the ken of Democrats and Republicans, but they might stumble upon the answer if they recast the question to an even simpler context. They could ask themselves: “If we have two people with diametrically opposed perspectives, read this as die-hard fans of opposing teams, being asked to make a fair ruling on a sports situation that occurred between the two teams as members of a nine-person adjudication panel how do you resolve their conflicting inputs?”

Spoiler alert! If you haven't figured it out and don't want to know (you know just like the Republicans and Democrats) don't read any further.
Solution: When faced with the question of who should recuse themselves, the answer for Thomas and Kagan is - "Just-us". Each should be willing to recuse their self conditional on the other agreeing to recuse their self.  It’s a modified version of “You cut, I chose.”