Different scholars mean different things when they discuss the role of law in judicial decision making. For post-positive theorists, all that matters is that judges sincerely attempt to find the best answer to legal questions. Jason Whitehead of USC just presented a fine paper presenting this view at the Law and Society meetings.
Jason’s paper aside, one problem with this approach is that it does not fully recognize the innate and largely subconscious human ability to convince ourselves of what we prefer to believe. If all that is asked by judges is that they sincerely believe in (i.e., have convinced themselves of) the appropriateness of their decisions, then short of Bush v. Gore, it’s hard to know when judges would fail this test.
I think we are better off conceiving of law as a potential and potentially measurable influence on judges’ behavior. To determine the impact of law is not much different than determining the impact of other social phenomena. Simply put, judges’ decisions should change -- not deterministically, but at the margins -- as law or legal arguments change, holding alternative phenomena constant. A recent example of this is a paper by Rachel Barkow of NYU Law school, who combines quantitative and qualitative methods to argue that a commitment to originalist methods leads Scalia and Thomas to support criminal defendants in non-capital jury cases far more often than we would expect given their ideology.