Relative pronouns that and which, usually taken for synonyms, differ subtly in sense; distinguishing their uses improves Clarity. Professor Geoffrey K. Pullum, who seems to have first noticed the difference, challenges the that-which rule, whose proponents assume these pronouns mean exactly the same thing; Pullum observes which is used more for conveying new or indefinite information in the pronoun's relative clause and that for established or definite information, but he reports only a mild statistical trend. (See http://tinyurl.com/yjnhhc7) Pullum's basis for distinguishing that from which contradicts the that-which rule, most widely recommended but designed for copy editors' convenience. The copy-editor's solution uses which to start descriptive clauses, that for restrictive clauses; that's occurrence confirms that the writer intended no comma before the relative clause.
Either the meaning distinction between that and which isn't weighty — Pullum's apparent view — or Pullum has missed the distinction's essence by recognizing a correlate. A more exact way to construe the that-which distinction applies which to parenthetical restrictive clauses, that to nonparenthetical ones. Since usage guides mistakenly equate "nonrestrictive" (or "descriptive") with "parenthetic," the notion of a parenthetic restrictive clause may seem nonsensical, but "parenthetic" and "nonrestrictive" name partly correlated but distinct linguistic properties . Restrictiveness concerns whether the modifier changes the reference class of the term modified; parenthesis concerns whether the information is incidental. Parenthesis admits of degrees; restrictiveness affects comma placement.
When instincts for pronoun choice fail, a writer can find guidance in the parenthesis test. Parentheses (the punctuation marks), like dashes, aren't confined to syntactic units. To apply this test, enclose the restrictive relative clause in parentheses. If the resulting sentence makes sense, then which is your choice, despite the absence of a comma. Here's an example of which being used restrictively but parenthetically.
An Originalist judge would likely rule that the patriotic originators, having won a war to preserve the Union, would not have intended to provide a law-breaking incentive which yielded no offsetting gain for the extant inhabitants.
To test, rewrite as:
An Originalist judge would likely rule that the patriotic originators, having won a war to preserve the Union, would not have intended to provide a law-breaking incentive (that/which yielded no offsetting gain for the extant inhabitants).
Since enclosing the relative clause in parentheses isn't illogical, which is the better relative pronoun. The information the clause conveys is marginal — figures as a mere qualification — even though the clause is restrictive.