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There are many commonly used phrases where hyphen is implicit and it's common to drop the hyphen.

p1: computer based approach

p2: computer-based approach

p1 is where the hyphen is implicit and is acceptable.

How ok is it to drop the hyphen in the first and last phrase of the following but include it in the middle?

Is the following acceptable, why/why not?

S: predatory patenting-versus-excessive process argument

In S, "predatory patenting" and "excessive process" are phrases common without hyphen.

Please don't just say it's ok or not and cite the style source

1

Your example would never be correct. If "predatory patenting versus excessive process" is being used as an adjective to describe argument, it should be "predatory-patenting-versus-excessive-process" in the strictest sense.

When you hyphenate as you have, you are explicitly separating the concept into three groups: "predatory", "patenting versus excessive", and "process", which doesn't make sense. An intelligent reader would probably be able to divine your meaning, but that should not be counted on.

As one example, the Chicago Manual of Style (16th edition, pp 331-336) is very flexible with hyphenation. When there is no ambiguity, it does not require any hyphenation. For example, "small animal hospital" is an ambiguous phrase: is it a small hospital for animals, or is it a hospital for small animals? If you mean the latter, you should use small-animal hospital.

In the case of a computer-based approach, the concept of "computer based" is fairly well understood to even a lay reader. This is because such a clause could never be misconstrued as "an approach for computers that's based" (whatever such a mouthful could mean).

In that vein, an alternative hyphenation scheme for your example that would be likely acceptable would be "predatory-patenting versus excessive-process". To make this more clear, think of the following example (without hyphens): "The red versus blue argument." The use of "versus" with "argument" is incredibly clear, and presents no ambiguity. In this case, we are clearly talking about the argument over red vs. blue. We could hyphenate red-versus-blue to reduce the possibility of some errant ambiguities, but it wouldn't be necessary.

To an informed reader, there may not be any ambiguity in the phrase sans hyphens: "the predatory patenting versus excessive process argument". However, that still is a five-word adjective, and a lay reader would undoubtedly benefit from at least a couple hyphens.

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