What can Professor Obama tell us about the next Supreme Court Justice?

The New York times is running an article about President Obama's style as a Constitutional Law professor at the University of Chicago. By all accounts he appeared to be a pragmatist, institutional structuralist who scoffed at the naïvete of apolitical legal formalism. With a sudden vacancy at hand on the Supreme Court, what does this tell us about an unnamed Justice to be?

From the article:

Mr. Obama often expressed concern that “democracy could be dangerous,” Mr. Stone said, that the majority can be “unempathetic — that’s a word that Barack has used — about the concerns of outsiders and minorities.”

But when a student asked Mr. Obama to name the circuit judge he would most like to argue in front of, he named Richard Posner, a conservative. Judge Posner was smart enough to know when you were right, Mr. Obama told the class.