What makes a legal question "hard"?

Question

When someone says another person has a brilliant legal mind, I assume that means the person is well suited for hard legal questions. I think mathematicians and logicians have a systematic way of determining how hard their questions are. Is there a similar way of determining how hard a legal question is?

From Computational Complexity Theory (Wikipedia):

NP-hardness (non-deterministic polynomial-time hard), in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP". More precisely, a problem H is NP-hard when every problem L in NP can be reduced in polynomial time to H.[1]:80 As a consequence, finding a polynomial algorithm to solve any NP-hard problem would give polynomial algorithms for all the problems in NP, which is unlikely as many of them are considered hard.[2]

A common mistake is thinking that the NP in "NP-hard" stands for "non-polynomial". Although it is widely suspected that there are no polynomial-time algorithms for NP-hard problems, this has never been proven. Moreover, the class NP also contains all problems which can be solved in polynomial time.

Answer 1

Questions of law can be hard when (among other things):

• the fact pattern has not been seen before (Bowman v. Monsanto),
• there is ambiguity in a statute (King v. Burwell),
• there is conflict between a statute and the constitution (United States v. Windsor), or
• there is apparently conflicting precedent (Campbell Ewald Co. v. Gomez).

Answer 2

There are many and innumermable reasons that a certain legal question might be considered "hard". The previous answer lists some of the more definitely-relevant ones especially "conflicting precedent"; that's often a situation that's particularly fruitful for giving rise to cases that are called hard.

But...there's kind of a big problem underlying this whole endeavor: the question of whether a case is "hard" is very often is a contentious battle between legal scholars/observers/commentators--and more importantly, between judges--itself. There really can be no firm, decisive set of criteria for dissecting whether a case is hard or not, because, generally speaking, to say "This is a hard case to me." usually means "In my mind, the question of which side should prevail in this case is a close call." And the sides can be close in a given jurist's head in a certain set of circumstances due to .... well, any combination of many, many, many factors.

In sum, in law even the question of what it means for a case to be "hard" is really pretty much impossibly hard. :)