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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.

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

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    I'll add to this answer: 1. Time-limitations make a problem more difficult and 2. Money limitations make a problem more difficult. – jqning Nov 9 '15 at 17:48
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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. :)

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