[Dogbert has been nominated to the Supreme Court:]
Senator: Do you have any opinions on the right to privacy?
Dogbert: No. In fact, I never formed an important opinion in my entire life.
Senator: You must think we're idiots!
Dogbert: Okay, I've formed one opinion, but that's all.
I personally would refuse to confirm a nominee who didn't give clear answers on how they would rule in various hypothetical cases. Furthermore, I would specifically point out their evasive answers meant they were either dishonest or incompetent, probably the former, and that's why I didn't consider them qualified.
On the other hand, I would not have any problem confirming a nominee whose opinions I disagreed with. Like many of the posters on The Volokh Conspiracy I believe that the Senate should give deference to the President's nominees.
One way of handling this would be to have a rule -- not a law but a "gentlemen's agreement" -- that each President is entitled to nominate one new justice to the Supreme Court. In other words, rather than a lifetime appointment, being a justice of the Supreme Court should be the equivalent of a 36-year term.
Like other "constitutional bargains" -- this is something we study in economics, specifically in my favorite field, public choice -- the idea behind it is that it treats both sides equally and neither of them knows whether they will be benefited or harmed by it.
If this were the case, i.e. if each of the last nine presidents had appointed one justice, it would be:
In other words, the court would be divided between five Republican justices and four Democratic ones.