Phone call the company during office hours[1], try to talk in person with the editor. An email is way too cumbersome, and slow, for such an urgent matter.
You clearly have all the rights to question the editor.
[1] your case is urgent, among the urgent things to be done by the editor in their dut...
dear downvoter(s), feel free to explain your downvote in light of OP sentence The letter contained two reports recommending publication and two reports, with negative comments, which have nothing to do with the manuscript, and possibly belonging to another manuscript and were submitted to me by mistake
"the company"? In my field, the editor is not an employee of the publisher but a professor in the field who is editing for free (or a small honorarium).
@AlexanderWoo the publisher is a company and has all the professional contacts to reach the editor, for business and working questions. If it is not a company, I wonder what is the utility of an Editor in Chief, see the experiences of diamond open access journal where such a figure is deprecated.
When the editor is working for free, a publisher has very little leverage to get them to be more responsible about their duties. Indeed, I know some journals where the Editor in Chief is an honorary position in which a well-known mathematician lends the prestige of their name to the journal but does little work, leaving the work to the Associate Editors. Over time, better run journals tend to attract more good papers, but a particular journal might not have a reputation to protect, and in any case, a small number of badly treated authors of rejected papers won't matter.
@AlexanderWoo in no points here is to be discussed the quality of the submitter paper, or of the review. According to OP, there have been a mishap at the Editor level (whatever Editor, in-chief or assistant or associate or slave editor), OP has one communication point with the whole editors pyramid, and they can get to that point by calling the publisher or whatever structure is editing the paper.
The editor is no more likely to DROP EVERYTHING AND RESPOND RIGHT NOW if the email is from an administrative assistant at the publisher than if the email is from an author. People have other things in their lives going on as well.
@WolfgangBangerth as I said, I do not disagree in general, but here the point is to get to talk with the editor. People have other things: an editor is an editor, it is very often paid to be an editor ( scienceguide.nl/2019/04/so-what-about-editor-compensation ) , it is in their TASK and in their DUTIES to be the contact point between authors and this immanent entity called "the journal". All the publishing bandwagon is already doing much less than what they should do, for the profit they have, let's not find excuse to them performin an inefficient and poor job (see OP question)
@WolfgangBangerth I realize I should explicitly write "Phone call the company during office hours ". Apologize, I am old-school and in the old times if you had something to get done remotely, you had to phone call, with the (at the time obvious) caveat that phone calls work during office hours, not this contemporary "remote working" crap where nothing can be done, because they removed from the "office hours" concept only the "hours" part, it remains the "office" part, without all the office infrastructures needed to employees to do a decent job.
@EarlGrey If you want to communicate with the editor, the best way to do that is to contact the editor directly. The company isn't really involved at this stage of the process - they are a publishing company, and the paper doesn't get passed over to them until it is accepted to publication.
@EspeciallyLime that would be wonderful, if only the editors leave the phone number in their email signature. The signature in the mail I receive(d) from the editors instead are usually something like: Ashok Kumar <name of publisher> and nothing else
@EarlGrey I've never heard of an editor being paid. I am not paid. If I made a mistake during the editorial process then I would try to fix it, but it still doesn't come above my actual job, or my family.
@EarlGrey I'm also not paid as the editor-in-chief of a mathematical journal, and I don't know anyone else who is. We're all just volunteers. But even if we were paid, it is just a job. People don'e DROP EVERYTHING AND RESPOND RIGHT NOW even if they are paid for a job. You've got to give people time.
@WolfgangBangerth I give people time, that's exactly what phone is there for: I call, if people picks up it means they have time, if they don't, they don't. There are way too many people sending an email and expecting an answer in a minute.
@EarlGrey I'm aware that academia varies. But your answer assumes that the editor is an employee of the journal and works at the journal. I think that's a very narrow slice of academia, where the editors aren't academics working at universities. And an admin mix-up with referee reports, which is probably what happened here, is hardly a major emergency needing phone calls and the cavalry.
@DavidA.Craven I am not assuming editors are employee of the journal. Do not put words I did not type in my keyboard. I am assuming editors are paid collaborator of the journal, and that the publisher of the journal has somewhere the (business) phone contact of the editor. There are loads of academics receiving all kind of moneys from the universities and from a variety of external sources. Regarding your straw-man about phone calls and cavalry, I hope you realize that the time you spend having an exchange per email is much larger than the time you would spend by talking with someone.
@DavidA.Craven regarding the very narrow slice of academia, I agree. Then there is a very large slice of academic editors that get paid by the uni and by the publishers. See tweet fom Tom Reller, who was vice president of global communications at Elsevier: twitter.com/TomReller/status/…
@EarlGrey Ah, so we are talking about editors in chief rather than editors. I am 99% sure that Elsevier editors in general don't get paid. Maybe the head editor does, I could ask a few and find out.
@DavidA.Craven am not focusing on a specific publisher. If you check Springer, they have an opening for an editor-in-chief, and it is paid: springer.com/journal/284/updates/23294020 as well as for general editors in applied mathematics: onetonline.org/link/…
@EarlGrey The second looks like an editor at Springer to me, as in, who works for Springer on book proposals, etc. All the publishing houses have them, I know a few of them from previous books I've written. The first didn't mention payment on it that I could see, but I'll take your word for it. I've not seen editor-in-chief jobs advertized in mathematics, personally, and the editorial boards I've been on have had changes of editors-in-chief without advertisements, or at least editors weren't alerted to them.
@EarlGrey This comment thread is why people are not expected to explain their downvotes: you demand to know the reasons for downvoting so you can argue with them.
@BryanKrause I am not expecting the people to explain their downvotes. I tell them they can feel free to explain their reasons. Can you see the difference?
Discussion on answer by EarlGrey: How…
Discussion on answer by EarlGrey: How…