I had another instance of what looks to be cheating on a take-home exam. See this post for the first case. It involves the same two students. The first time I couldn't be sure if they were cheating or just working from close notes from class. They didn't even answer all of the same questions, but the ones they answered in common (maybe 60-70% of them) were very similar. They tended to start out with identical wording, but it was because it was based on the exact wording of the question they were answering. From there the answers tended to follow similar paths but with different wordings from each other, sometimes with a sentence by one that wasn't close to anything in the other but largely consistent with working from the same outline as each other, which is what I'm guessing happened. I couldn't rule out that they had simply availed each other of each other's class notes, which I told them they could do as long as they didn't help each other arrive at their answers in any way further than that.
Well, the third exam came along, and I was right to be suspicious. The same two have submitted exams that are very similar again, but this time they did exactly the same questions. I'm guessing that they did work together on the second exam and figured I didn't notice, so they went all out this time thinking they'd be home free. The sad thing about it all is that their answers tend to be among the best in the class. I think it would have been immoral to fail them the first time, given that I couldn't really have ruled out an alternative explanation besides cheating, but it seems to me that the second time gives me enough evidence to do something.
I've decided not to fail them outright. I'd like to encourage them to come forward and admit it to me, so I'm offering a lower penalty for them if they come forward. I'm going to tell the class the basic information about the first and second occurrence and why I did nothing the first time but think it's too clear now the second time. I'll then say that I'll give half credit on each exam to each student if they don't come forward (after all they did presumably each do half the work; both are good students, as demonstrated by other work). That will still be a failing grade, but it won't be a zero. But if they come forward I'm going to be willing to let them improve their grade by answering more questions to be able to avoid failing. I won't have graded the exams yet when I say this, so they won't know if they're the ones I'm talking about, and it really will be on them to come forward. I think this is a strong enough warning to them to show that cheating is serious while giving freshmen in their first college experience a chance to make up for it if they're honest about it and willing to do the work they should have done in the first place.