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 "free rider". 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.