These two documents will help you to more easily implement the Socratic Seminar (also known as a PAIDEIA Seminar) and to fairly grade each student's participation in the seminar.
I use these when holding Socratic Seminars with my 7th graders in my ELA class. I review the guidelines and the rubric each time I announce that there is an upcoming seminar. Each student has a copy of the rubric to know what to expect regarding grading. I take notes during the seminar based on each student's participation. Afterwards, I make copies of the rubric. Each student receives a rubric with the grade they received on the seminar--I highlight the grade and also highlight areas that need improvement in order for the student to be able to better his/her grade the next time we have a seminar. (Socratic Seminars or PAIDEIA seminars are quite effective in teaching aspects of ELA Common Core standards.)