Having team-members split the grade among them by their personal contribution In a project-based class the submission is in teams of 2 (self-assigned teams).
In most teams, the grade is the same for both members.
However,  in some teams, I suspect that most of the work was done by one member, while the other was a &quot;free rider&quot;. The suspicions are based on GitHub commits and on interaction during the semester. However, I do not have clear-cut proofs since I do not know how they split the work among them at home. I can test them personally, but this is not sufficient since it is possible that the free-rider knows what the other person did.
I am not allowed to change the grade structure in retrospect, so I thought of an idea that is based on mutual agreement: if the grade that the team deserves is X, I will tell them that their total grade is 2 X, and ask them to agree on a fair division of the grade among them. If they do not agree, then the grade is just split equally between them as usual. Effectively, this gives the free riders a chance to behave fairly and give some points to their friends who did most of the work.
The advantage is that the team members know much more than me what work each of them did. The disadvantage is that this may cause quarrels among team members. Is this a good idea?
EDIT: Thanks for all the answers. I am now convinced that this scheme might create psychological and social problems  that are better avoided.
A problem I see here is that this scheme may motivate people to divide the points &quot;tactically&quot;. Say our group project is worth 10 points and I only need 5 for my goal (which may be the least passing grade or the best grade or whatever). Then of course I would take only 5 points and give 15 to my collegue (which is more than the project is worth).
Also, it might motivate people to look for their partners tactically: If I am somebody who does not trust other people and wants to do everything themselves (something which should ideally be discouraged in group projects), I choose the person who cares least about their grades as a partner and get much more points than my project is worth.
Moreover, with this setting, you treat the grades as some currency. students will find it okay to do less/more work because they can themselves discuss and haggle about the grade they got. IMO this is also not something which should be encouraged.