Look : my first quarter as a TA I had not explicitly written out instructions on re-grading, and would have students arguing for fractions of points. I’d end up giving back points that I didn’t think they had earned. I had a great professor in college that required us to write a paragraph on why we thought we should get a higher grade, and submit that paragraph with the original work for an entire re-grade. This meant that we could get a lower grade overall, but it also reduced the number of re-grades, and any face-to-face arguments that you might regret later. I adopted this policy, and had no problems later on.
