Suppose I write a paper and you write a paper of the same length. But then I plagiarize your paper using the following procedure. I look at the first character in our papers, and if it’s different, I erase (unless it’s a space) the character in my paper and write down the character you had in its place. And then I repeat for the second, third, and so on. I then submit the paper for publication.
It seems clear that I’ve plagiarized your paper in its entirety, even though some of the letters in my paper weren’t erased as by coincidence I originally had the same letter in the same place as you did—this will happen more often with more common letters like “e”.
But what if, by chance, your paper and my original paper were verbatim the same, and I never noticed this? Then the paper I submit for publication depends for all of its content counterfactually on the paper you wrote, but not a letter was changed from the paper that I wrote. If authorship is defined by causation, then the paper I am submitting is my own. If it’s defined by counterfactual dependence, it’s yours.
I don’t know which is the right answer.