Journal published a paper, ignoring my objections as a referee

EDIT: The question has been changed since this was written.

Your key misconception is that the editor needs reviewers' permission to publish a paper. Actually, the decision to publish rests solely with the editor.

In this case, you disagree with the editor, but we do not have enough information to tell who is correct. If you think the errors in the paper are important, then once the paper is published you may be able to submit a comment to the journal. Do not do that before the paper is published, because for most journals you must maintain the confidentiality of peer review.

This probably isn't something to fight over. Possibilities abound:

• Perhaps you misunderstood something.
• Perhaps the other reviewers were positive on the paper.
• Perhaps the authors provided arguments that your rejection reasons aren't applicable, and the editor found them convincing.
• Perhaps the editor thinks it's better to accept a potentially bad paper than to reject a potentially good one.
• Perhaps the authors said they cannot fix the issues (e.g. funding ran out, one of the lead experimenters graduated and is no longer in the group, etc) and the editor made the judgment call to accept anyway.
• Perhaps the journal is short on papers to fill its issues and so is accepting borderline papers.
• Perhaps the editor simply made a mistake, but since the paper is already accepted, decided to stick with accept instead of rescind the decision.

Ultimately journals are going to publish whatever their editors think are acceptable. Reviewers do not "give permission" to publish something; they only offer recommendations. In the same way if there is a backlash against the journal for publishing this paper, it's the editors who take the heat, not the reviewers. So even if your objections are correct, it's probably still not something to fight over.

If it really bothers you, you could email the editor asking why they accepted the article in spite of your comments. If the response they give isn't satisfactory, you could refuse to review for and/or publish in this journal in the future. If it really bothers you and you feel taking retributive action against the journal is justified, you could try denouncing the paper on social media (high-level summary of what happened), but be psychologically prepared for the drama that might follow.

Alternatively, you could view the entire episode positively - hey, I can now write a paper arguing why this paper is wrong!

tl;dr: You may want to send an email to the editor about this. Although it will not change anything about this paper, it will be a good lesson for the editor to engage in more constructive correspondence with referees who are spending a lot of effort for free to enable the existence of the journal itself, as well as to be more responsible in his/her decisions next time.

--

This is something that can and does happen in reputable and even prestigious journals. We do not have the full picture, only what you wrote, but based on my experience, I tend to believe you are correct, and the editor made a judgment that takes into account non-scientific factors such as:

• Efficiency. He/She does not have time to deal with the details too much. He/she needs to make a fast decision and it's safest to let the paper in because it was on a fast pace track anyway.

• Politics/Importance/Perceived-importance of papers/author. Since it was on a fast track the paper was probably important for some reason to the journal/editorial board. Maybe it gives them some prestige? Or whatever reason. The editor knew there is a reason for concern, but went with publishing it because he/she decided to ignore what they perceive as "details" that "do not take into account the whole picture", or something like that.

• Possibly, the editor did a genuine decision, believing the paper merits acceptance, and that "you are just picking on the details". They may have a different view than yours, they may think that details are unimportant.

Overall, I tend to agree with your view: details are extremely important and decisions should be made based on objective merits solely as much as possible. Unfortunately, that is not how the system works.

Conclusions: You may want to fight a bit over it. I don't see it as harmful. Simply send an email to the editor to inform them that you think they made a wrong decision as long as the reviewers don't address your concerns. This will not change anything for the present paper, but for the next paper this editor will be more cautious I assume. He/she may be a bit pissed off by your email, but so be it.