Suppose that a paper is submitted to a journal and that the editor decides to sent it out to two reviewers. Each reviewer agrees to return the report in X months; however, it turns out that one of them is much faster than the other. The editor thus receives the first report, which firmly recommends rejection. The editor does not wait for the second report and rejects the paper.
How common is this scenario? For what is worth, my field of interest is mathematics.
No, it is not common, but a strong reject for reasons that cannot be resolved in the eyes of the editor is sometimes sufficient. Ultimately, the referee that is most important is the editor and their vote is the "loudest". They don't have to take the average of the referees and can override it.
It is important to look at what the reviewer has said. It is likely the commentary is highlighting serious errors, either mathematical, conceptual, or in presentation. The editor appears to have agreed and no longer can spend reviewer time in good faith.
I have certainly done that, and I think it is totally reasonable: If the first reviewer gives good reasons why the paper should be rejected, then it is quite unlikely that anything the second reviewer can possibly say would make me change my mind. That first reviewer might have been the world expert on the topic (which the editor would know), so what good would it do to wait for the second reviewer other than (i) artificially prolong the process, (ii) waste the second reviewer's time.
So while this might not happen in a large number of cases, good editors do it and do so for good reason.
