How do we resolve author ordering dispute for rewritten paper with new contributor and less contribution from original first author?

Question

(note I work in a field were author ordering is important and is meant to reflect relative contributions). The situation is the following:

Me and a colleague (who I will call C from now on) independently conceived of a research idea. I joined C and two other colleagues who had just started working on the idea. In the months that followed, I ran the majority of the experiments and wrote most of the code; C wrote some code in the first 2 days and was active in discussions / planning afterwards, and also ran two experiments (i.e. ran the code written by me and colleagues).

When we decided to write up a paper, C proposed that we be co-first authors, with him being listed first. I agreed. He wrote most of the related work and discussion section, and I wrote most of the rest of the paper (in both cases 'most' meaning roughly 'everything apart from ~2-3 paragraphs').

The paper was rejected from a conference. A new person joined the project; we ran a number of new experiments and re-wrote most of the text of the paper, including most of what C originally wrote. C contributed in small ways to the second iteration (e.g. making a figure from data that I collected). ETA: To clarify, C agreed to the addition of the new person as author, and he was actively supportive of the idea of re-submitting the paper, doing new experiments, and re-drafting sections. Unfortunately we did not discuss a new author ordering before submitting the revised paper (this was obviously a mistake).

The updated paper has now been accepted to a conference. I and all authors apart from C think we should probably change the author ordering (currently me and C are co-first, with C listed first; personally, I believe that I and another author both contributed more than C). ETA: The other author who I think contributed more was involved from the very beginning (and proposed the flagship experiment), not the new person.

There are a few complications:

• We already publicly posted the first (rejected) version of the paper on arxiv, with C listed first.
• C vehemently disagrees with changing the author order
• C also does not want to discuss this or talk to an external mediator
• C may be having mental health issues

What is the best way to proceed here? The ideal would have been to find consensus, but that seems unlikely. We are considering getting an external mediator involved even though C may not be willing to talk to them, as they may be able to provide a somewhat objective opinion and I want to avoid taking a decision unilaterally. Is there anything else we can do?

A key point here is that I am worried that C cannot currently represent his case as fully as he could otherwise due to mental health issues.

Some possible outcomes:

• We leave the author order as-is.
• We leave C as co-first author, but make my other colleague co-first author as well and change the listing order.
• We make the strongest change, making me sole first author and C third
• Something else?

Answer 1

There's a bit of a gap in your narrative around:

A new person joined the project; we ran a number of new experiments and re-wrote most of the text of the paper, including most of what C originally wrote.

From my perspective outside your group of authors, it sure sounds like C got pushed out of the way and you expected them to be okay with not having the same role in the paper anymore. It seems like you did this without C's blessing or agreement. Even if they were moving slowly or someone else was itching to get things done, your original agreement with C holds until you renegotiate.

The better time to negotiate this change would have been before the new person came in and did a bunch of work.

You have to reach an author order that everyone agrees with, so you don't get to choose from the possible options you've listed, you only get to come to agreement with your coauthors about one of them.

I'd be careful about referring to C's mental health in any of this. I don't know if you mean to imply that their mental health is somehow making them stubborn or unwilling to cooperate, or that the reason you pushed them aside is because of their mental health, but neither argument looks good for you.

Answer 2

Generally you have to resolve author order co-operatively since any author can refuse to let the paper be published. In reality, however, power relationships come in to play and subordinates often yield to superiors, whether fairly or not. And, since any one can stop publication, one jerk can foul up the process if they like.

Trying to drop an author can leave you with plagiarism issues.

You had an agreement originally. I'd guess that the best, certainly easiest, solution is to just maintain that. It gets you over the hump and you get a publication as does everyone else. Copacetic. A publication is a good thing even if you aren't as high in the author order as you think proper.

Very few careers depend on author order of a single publication.

And, in future, discuss these things early on and probably avoid working with C, at least.