Do editors ever "overbook" referees? Is the following common? An editor for a journal sends a paper out to, say, three or four referees. After getting the first two referee reports, the editor makes a decision and tells the third and fourth referees not to bother (so that they have potentially been wasting their time).

I can see this happening in some circumstances, e.g. if one referee finds a substantial error. However, I was asked to referee for one journal, and I get the impression (which I have not yet confirmed) that they typically send the paper out to lots of referees and take only the first couple of referee reports.

This practice, if it is indeed what they are doing, seems likely to produce quick turnaround times, but also seems disrespectful to referees who might be half-finished when they are told their reports are no longer needed. 

Is this common? (In particular, in mathematics?)
I think this one will be very hard to answer with hard data. So, I'll just throw in some anecdotal evidence, along with a few things learnt from some editors that I know.

From a reviewer point of view, it has happened to me exactly twice in a decade (i.e. very rarely) to receive an editor's review saying “I've reached a decision based on input from other reviewers, and you do not need to review the manuscript”.


The first time, the email came as my review was already overdue (a week or ten days), so I suppose the editor asked another reviewer when I didn't reply on time, and the new reviewer was fast to reply.
The second time, it was sort of the other way around: I was asked to review a paper, then 5 days later the editor wrote, saying the reviewer who was uncommunicative had finally replied, and my review was no longer needed. He apologized profusely, and offered to actually wait for my review if I had started doing it and wanted to finish. (I was happy to let it go.)


I think for an editor, growing a list of trustworthy and willing reviewers is crucial. So, they simply cannot make them work for nothing! (pun intended)