As a TA we did something similar: we asked them to self grade their own homework using a provided rubric, and then we spot checked 1/4 of the students (without replacement) to punish lying about what grade you deserve. We didn’t punish for a few disagreements over the rubric, but if it was blatant we checked their assignments every time in the future (and told them). I think if it was bad enough we could have reported them.

This saved a bunch of time on actually grading assignments and made us write a very clear and unambiguous rubric (which required a very clear homework) and also demonstrated to the students that grading was not arbitrary.