Is it ethical/acceptable to give a lighter penalty to students who admit to cheating? I am at the moment dealing with an academic dishonesty incident in a class I'm teaching (a few groups of students submitting identical code, when the class policy forbids getting help from another person on a graded assignment).

When I noticed indications of plagiarism, I emailed each affected student something along the lines of:


  The code you submitted is nearly identical to another student's work. Can you comment on this?


Their reactions mainly fall into three categories:


"I made a mistake and I take full responsibility for it, I hope you will let me make it up but I understand if you can't."
"I talked about the assignment with another student, but I didn't copy anyone's code." But then when I inform them they're getting a zero grade for the assignment, they don't argue.
"I didn't do it! You can't give me a zero grade for the assignment when I didn't cheat, I refuse to accept a zero grade."


Assuming I have evidence that all of these students cheated, is there a good reason to adjust the penalty based on whether students own up to their misconduct, or continue to lie about it?

On the one hand, I appreciate honesty, and doubling down on a lie seems like something that should be punished. On the other hand, I've never heard of anyone adjusting penalties like this, so I'm wondering if there's some reason I shouldn't. 

It's also not clear to me what the relative difference in penalties should be, if there is one. I thought about it and it's hard for me to come up with one penalty that's appropriate for Group 1, another penalty that's appropriate for Group 2, and a third penalty that's appropriate for Group 3.

I would very much appreciate answers based on research and/or experience with policies like this, rather than just opinion.

(My school has no official policy on the matter.)
TL; DR: We adjust the penalty.

I sit on my department's Academic Misconduct Committee so unfortunately I see a lot of these cases. The University policy has created two similarly sounding, but different terms: academic misconduct and poor academic practice, with academic misconduct being much more severe than poor academic practice. Every student suspected of having engaged in poor academic practice is called into a meeting with the Academic Misconduct Committee. This committee looks at the evidence supporting academic misconduct/poor practice and hears the student's case which generally includes what training they have had about good academic practice, how the incident happened, and any evidence of extenuating circumstances (e.g., death in the family). 

Based on this process we can come to one of 3 decisions: 


not poor academic practice, 
poor academic practice, 
academic misconduct. 


If we decide that they did not engage in poor academic practice, the incident is essentially purged from the system. If the student is called in again in the future, we do not nominally know that they had been called in before. If we decide that it was poor academic practice, the students are warned and it is documented. We are not allowed to apply formal penalties in the case of poor academic practice. If they are called in again we know from the documentation and are unlikely to give them the benefit of the doubt a second time.

If we decide that academic misconduct has occurred we can apply one of a number of different penalties to the work: no reduction of the mark, remark the work with the offending material removed or reduce the mark commensurate with the misconduct (anywhere from a 5% penalty to a 0 for the piece of work). A second incident of academic misconduct results in the penalty being decided on by a university panel and starts with a zero for the class and can go as high as a zero for the year. In this way there is a big difference between poor academic practice and academic misconduct with no reduction in the mark since poor academic practice does not count as a first offense.

Within this framework the committee is faced with how to handle the students who admit the issue and the ones who deny the issue. Those who argue they didn't cheat and have no explanation as to how their assignment matches another's work are almost always found guilty of academic misconduct since they are not willing to help us create a case for poor academic practice. More often than not they receive a 0 since we have no evidence that mitigates the penalty. For students who admit what they did, we often consider poor academic practice as an outcome since they describe what they did and realize it was wrong. Sometimes the offense is too blatant to let off without a reduction, but generally saying what you did wrong and how you will not let it happen again reduces the penalty.