Different tools for different purposes
It's not that I don't understand that voting to close and up/down-voting do - or imho, can - signal different things and do (can) have different functions. Close votes are meant to indicate that something is off-topic for the site, irrespective of the quality of the question (one reason often given is that "a bad-fitting question will lead to answers that don't fit the site, either"), whereas down-votes indicate an opinion on the quality of the question (for many potential reasons). Therefore they can certainly be used to send different messages and accomplish different things.
That is exactly the point; they must represent different things. It is not my experience that all users do use them in the intended way, hence Close Votes Aren't Super Downvotes, but that does not mean the rest of us shouldn't try.
Up/Down voting is a subjective measure of the overall quality and helpfulness of a question. It should be done after you have determined whether the question is on topic. You should be aware what kind of signal you are sending as in most of the cases this is a completely silent action.
Closing questions (except as duplicates, see at the end) is a measure to prevent questions (and by extension answer) of a subject matter that has too little links to the core topic of the site. The (current) homework policy is already stretching this, which is evident by the long struggle coming up with a substantially better solution, but it is a necessary extension of the concept. (Any discussion of that part would fit in one of the other discussions better, so I am not going to treat that any special further on.)
Thing is that, as I understand it, if I regard a question as being irredeemable [...] I should vote to close this question.
I find this viewpoint too negative. In my opinion, this is the wrong motivation to treat any question. Irredeemable sounds like a doomsday, never to return scenario. I think this is conceptually wrong. The majority of closed/held questions is redeemable, which is why the are not closed initially, but put on hold. Only if the OP (or by extension the community) decides to do nothing it is closed. That doesn't change the fact that such a question could still be 'redeemed' (or I would prefer polished, refit, and reopened).
You should vote to close a question if it, in its current state, does not fit into the scope of the site. This should be done as objective as possible. Bonus points to anyone pointing out the weak points in the question, so that it can be improved and reopened.
Closing questions is effectively putting them in improve mode or shortlist them for deletion.
If a question is indeed irredeemable, then why actually bother putting it on hold. A better action would be to down vote and move on. I might get to that later.
Therefore this is in effect akin to a "super down-vote", not in the reputation sense, but because, as I understand it, "bad" questions may belong to the subset of close-able questions (again, particularly when defined as irredeemable, where no extent of back-and-forth commenting and editing would be expected to rescue the question).
Again, I think irredeemable is the wrong line of argumentation, and the wrong interpretation, especially because it somewhat counteracts the benefits of closing.
I disagree that "bad" questions are a subset of close-able questions. I do think there is an intersecting set of questions that are "bad" and off-topic. Here for example is a badly received question, which is not off topic: Does berylium gain or lose electrons? (Warning: This might eventually get cleaned up in some way or the other.)
And ultimately, both close-voted questions (unless reopened) and severely downvoted questions will end up deleted (in my understanding of how the site works) or forever ignored, which is functionally the same fate.
Yes, for obvious reasons, questions from both categories are less desirable to have around and will (often) get cleaned up. It is not the fate of every closed question though, not even the fate of every negative scoring question. The deletion mechanisms are quite conservative, and much fill be retained even though it might not be worth it.
If we were to strictly follow through, then yes, these questions were to be deleted; who would keep around something that is deemed unhelpful or not on the same topic of the site.
So, this makes me wonder why we make a big deal about the differences rather than the similarities between the processes? Provided we understand that the range of application differs for the two tools, why not call the close vote a "super-down-vote-without-reputation-penalty" in situations where the term applies?
Because that fundamentally undermines the system. If a question is not off-topic it must not be closed. And just because in some of the cases the final state is the same, there are not nearly enough similarities to even equate parts of the process, after all a dead cat lived a live as a cat and a dead Schrödinger thought-experimented on animals.
Obviously there is a caveat: With the homework close reason and its somewhat fuzzy edges, closing questions already got undermined in a way. It introduced a grey area, where seemingly on-topic questions get the off-topic treatment.
I apologize if I should have revisited the site guide before posting this, but as I see it the meta posts are not that instructive.
It is never too late to learn, and it is better to ask twice than never at all. Also, information is scattered and not well enough to find. I found the help page on voting a bit instructive, and the help page on closing quite good. There is much, much more information on "mother-meta": FAQ for Stack Exchange sites. Like What is a "closed", “on hold”, or "duplicate" question? or When should I vote?
There is also A guide to moderating chem.SE yourself - close voting
Summarising the above, closing questions is a protective measure aimed at improving these, therefore it is accompanied with (at least) a short message. Up- and down-voting are judging measures, which are (mostly) silent. They can be combined, and also used in conjunction with comments.
... (say because it is a duplicate - this being a lesser offense) ...
Duplicate closures are a special case. This reason somewhat stands alone. You (a non-moderator user) can only choose this option if a question with an answer exists. A question closed with this option usually is on topic. It can also be very good, and duplicates (even not so good ones) are retained longer than other questions.
See for example
The reason for this somewhat special case is that you can ask questions in different ways. The answers will still be applicable true for both cases.
(Moderators can also pick targets without answers, and we do, if they are almost identical, to avoid duplicating effort and having to merge later on.)
BTW This barrage of repeated questions on the same topic provides a potentially good test of teh mechanisms available to edit/screen questions:
- finding the density of compounds
- calculate the lattice structure of UC4
- Find the theoretical density
Should these questions be down-voted or closed, and, what's the difference?
- Finding the density of a chemical compound (self-deleted, 10k reputation necessary)
Actually they are not a good test of the automatic mechanisms, as they require to be handled manually with (at least at some point) mod-powers.
As for the question itself, I definitely think it can be reshaped and made a good fit for the site. Certainly not a top-scorer, but generally helpful, even only for a niche group of people. (That being said... we can count the second for the meta-effect to kick in.)
Number 4 is actually the first in the series, followed by 3, which is the same but shortened. That was pointed out, and with the addition of the comment by the OP comes back to the same content.
Since they are basically the same question, they should be closed as duplicates. If there were answers or comments, the should be merged by a moderator.
Next was 2, which is a somewhat different take on the same problem, and quite possibly a manifestation of the XY problem. I personally do not regard this as a good question, ergo I down-vote. Additionally I think it needs more context. I would not argue with anyone who thinks this is too broad.
On the other hand there is already some discussion on the topic, so this could definitely be made into a better fit.
Last was 1, which is basically verbatim 3,4, and therefore rightfully closed as duplicate. Again with comment threads or answers, merge would be the way to go.
The whole thing is problematic, because we are dealing with an impatient user, and things unfold quicker (4 questions in less than 4 h) than any automated or as helpful intended process could take a hold on this. In the meantime the user is blocked from asking, and I would not be surprised to never hear of it again.
As such, this will probably soon be abandoned and as a consequence of score be deleted.
Why bother with closing terrible questions?
Earlier I wrote that if a question is irredeemable in my eyes, I probably wouldn't bother to down-vote, and I encourage everyone to do the same.
If there really is no chance to breath life into a question (I doubt it), then it should be deleted, hidden, not pushed to more users. A close vote will put it in the queue and possibly 4 more users will have to look at it. Even a trivial edit would put it into the review queue bothering more users. All the time taking up space on the homepage. I think most of us know which kind of questions fall within this category. (And I still think that many of them could be salvaged.)
A quick enough way to deal with them is to down-vote them, with a score lower than -5 they get hidden. And who knows, they could still encourage someone to answer brilliantly and get lifejacket or lifeboat.
I think that a generally more positive attitude towards questions could be beneficial.