Amendment?

I’ll probably have more to say about this post later, but one thing I would say is that I don’t see why you would need a constitutional amendment to change the voting rules of the federal courts. Nothing in Article III establishes a voting rule, and Congress has the statutory authority to regulate the courts. If it wanted to, I don’t see why Congress couldn’t require a supermajority to overrule lower courts (although I agree with Matt that definitional problems would arise from limiting this to constitutional cases, as what seem to be constitutional cases can often be turned into nominally statutory cases.) At the very least, such a regulation would have a very strong constitutional argument on its behalf.

This won’t happen, though, partly for the reasons suggested by the fact that most judicial power in the United States derives from statute and the acquiescence of the other branches: judicial power frequently serves the interests of political actors.