# What makes a legal question “hard”?

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.: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.

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.

• As a mathematician, I can tell you that we really don't have a systematic way of determining how hard a question is. It's very subjective. I expect law is the same. – Nate Eldredge Nov 8 '15 at 15:01
• I edited my question to show the example of "np-hardness" – Mr. A Nov 8 '15 at 18:58
• @Mr.A NP-hard is a technical term about the time it takes a computer to solve problems in a certain class; the problems are in fact often very easy to solve, just very slow. Trying to make that analogous to whether a legal problem is difficult is like drawing an analogy between an irrational law and the square root of 2. – cpast Nov 8 '15 at 19:52
• @NateEldredge it is very much the same. In fact, lawyers, judges, and legal scholars will have fervent debates about whether case X is "hard" probably about as often as debates over what the actual outcome of case X should be. Indeed, very often it's true that if you were able to know whether Justice John Smith thinks a case is "hard" or not that would greatly aid your assessment of which way Justice Smith will probably vote on the outcome of the case. (If that makes sense.) – mostlyinformed Nov 9 '15 at 8:42
• Justice Potter Stewart's obscenity definition sets the precedent: "I know it when I see it" – user662852 Nov 9 '15 at 13:45