Should a prosecutor-turned-justice recuse in an appeal on a case where he sought the death penalty?

From NPR News:

The U.S. Supreme Court hears arguments [today] testing whether a Pennsylvania Supreme Court justice violated the U.S. Constitution when he ruled in a death penalty case that he had been involved with as a prosecutor.

At issue is whether then-Chief Justice Ronald Castille, by refusing to recuse himself, denied the defendant, Terrance Williams, a fair hearing.

Full story and link to the audio clip here.