Before we get to the sentence in question, let's look at the first use of passive voice in the article. One way to do that is to read each of the headings in the article:
Express actions in verbs
Avoid strings of prepositional phrases
Choose clear subjects
Favor active voice over passive voice, using passive-voice constructions with intent
Avoid beginning sentences with expletive constructions
and so forth.
All of these are instructions. They are not unlike instructions found in a recipe:
Preheat oven to 375
Coat cake pan with butter, then dust with flour
In instructions, articles are often dispensed with.
So what's going on in
Note that passive voice is more prevalent and accepted in some disciplines (e.g. some sciences, public policy) than others. [?]1
I don't particularly like this non-use of the definite article here. Perhaps the writer sticks with it because he/she has used it in the heading, which we have seen is an instruction. When we have to start questioning why a "Writing Studio" on Clarity and Conciseness has written something in a certain way and there is no explanation, I wonder how great a style sheet on better writing it is.
The anarthrous use of passive voice can be thought of as an ellipsis for (the) passive voice ((construction)). I am not too happy with that idea, because it seems all too easy to explain certain uses by recourse to the E-word. But passive voice does have a kind of, sort of-ish "proper noun"-like role here. We don't usually use definite articles with proper nouns (except when part of a name: the UK), since a proper noun is already identifying which thing we are talking about. But I don't like this explanation. What I do like is to look at passive voice and active voice as two modes a sentence can have. Not in the grammatical sense, but more like in the electric shaver sense. The electric shaver is either on or off, and
Note that on is more prevalent [than off] in some disciplines...
is one way of looking at it: both passive voice and active voice are two "binary modes," like on and off.
Driving with heater is more prevalent than driving with air-conditioner in some climates.
Speaking of driving, let's switch gears and look at the first Economist usage you give:
Pity the passive voice.
This looks like an instruction. If it is, then why does it use the article? Didn't I just say that in instructions we often omit the article. Well, yes, we often do. But not here when it is the opening line of an article (that other kind of article). If the article had opened with
Pity passive voice.
It would sound too much like like a telegram or a headline, and we've gotten past the headline here, although I can't get past the headline to your second Economist link because that's all I see there.
But when might this nifty three-word sentence be used? (pause for reflection) It might be used by a student who is taking notes while reading the article, or listening to an audio of the article. Since notetaking is another place we dispense with articles. Again, just as with proper proper nouns (no, that repeated word is not a typo), and with instructions, the article in notes can be done away with, precisely because the speaker/writer/reader knows which referent we're talking about. This grammatical explanation may not stand up to the most assiduous scrutiny, but consider
Open mouth, insert foot.
This is an instruction to oneself after making an idiot remark to someone. The self giving this instruction knows which mouth and which foot he/she's talking about.
I now return to
Note that passive voice is more prevalent and accepted in some disciplines (e.g. some sciences, public policy) than others.
If I were sitting in class and if these incredible writing tips were being lectured to me rather than written to me, I just might take a note and, just like for Pity passive voice, I might write down Note that passive voice... That is just one way to explain this usage, and if I recall correctly I've explored a couple other ways here too. But like I said, I'm not wild about the anarthrous usage here, and to me it would read much more naturally were the precede passive voice.
I feel like I should put a question mark somewhere, since I am asking a question (So what's going on in..?
) but I dunno how or where, and I am not going to avoid the issue by using a work around.