Is it ethical to slightly improve upon someone's work posted in arxiv and publish before the original work, however citing the original work?
I mean suppose the original work gets rejected in a top-tier journal (generally top-tier journal takes so much time) whereas the improved version gets accepted in a mediocre journal (suppose the mediocre journal is fast in reviewing).
Then what should the author of the original work (I am the author of the original work) should do?
I question, as did Dan Romik, your characterization of work posted on arXiv as 'unpublished': it is made available to what amounts to the widest possible public, it is just an un-refereed publication (or perhaps arguably a kind-of very slightly refereed one, if you read the conditions).
I suggest that the ethics of it depend on whether the later-published paper acknowledged the arXiv paper as earlier work, or not. If it did, I see no problem.
If the later paper made no acknowledgement, then maybe there is a problem if its editor/referee(s) happened not to spot the earlier paper in arXiv and took the whole content of the later author as original.
But what the arXiv author could do in that event I could not begin to suggest. Best response would probably depend highly on the particular circumstances, which would no doubt be awkward to set out in this medium.
As long as you cite the prior work as such and make it absolutely clear what their contribution is relative to yours, then I think you are fine from an ethical standpoint. Papers on arxiv are published in the literal sense of the word, and there is nothing unethical about following up published work.
However, you also want to avoid annoying the other set of authors. The easiest way to do that is to get in touch with them and perhaps ask for feedback on your draft.
Unfortunately, this can be an awkward situation. Some people say they only post on arxiv after their paper is accepted to avoid people following up their work before it is accepted. The first paper deserves full credit.
TLDR: Be generous with giving credit.
I think the best solution here is to contact the original author. You do not know if the paper was submitted to a journal, what stage of review it is. Who knows, it might be already accepted and will be published tomorrow morning.
How about something along the lines of:
Dear Author Authorson,
I read your work titled "The almost most magnificent work ever done" published on arxiv, and I enjoyed it very much because it is relevant to my work on ABC and it can have implications for DEF. I wanted to ask you several questions.
I have found that by applying the method of X and adding equations Y and Z, the uncertainty is reduced by half. (you might want to be vague enough here to not disclose exactly how you did, otherwise the original author might scoop you on this) Have you thought about this option?
Is your paper submitted? What stage is it in? If possible, I would like to collaborate and potentially improve the paper to make it more suitable for XYZ.
Ideally, this might result in a joint publication for both of you. A win-win situation.
A huge chunk of academia is about improving others’ work, whether by independent verification of results, pushing the research envelope, or correcting errors in prior work.
A work that is based on an earlier work should cite it, and clearly mark the point at which the new work begins.
I see 2 question’s posed, with the scenario that E edits O’s original work W1, cites W1, then publishes the edited work W2. W1 is publicly accessible (as opposed to a private letter or similar).
Is E being unethical? If E marks the new work clearly, then that should be fine (think of it as a lit review of sorts). Otherwise, they’re trying to pass off someone else’s work as their own - that’s unethical. Sooner or later, one would expect that the similarity between W1 and W2 would be noticed, especially since W2 cites W1.
What does O do? In the ‘lit review’ setting, O can do a happy dance at being cited. This is academic success - someone thinks the work is good enough to take seriously. In the plagiarism setting, O can write to the publisher of W2, referring them to W1.
Credit to Dan Romik for noting that Arkiv isn’t “unpublished work”, and that credit ascribed to the subsequent author is proportional to the significance of the new work.
No, publishing someone else's work is plagiarism. It does not matter if that work has been improved or if it is unpublished. It is still plagiarism if you cite and acknowledge them. It is totally irrelevant that the prior work is on ArXiv.
You can publish the improvement, but you must not include someone else's work.
