Letting students grade their own homework
I have used a similar technique, albeit in a course for nonmajors and at a time late in my  career when I was willing to acknowledge that my grading was often pretty impressionistic even when I had a rubric.

To maximize what students learned from homework and to minimize the time I had to spend parsing their answers, I would go over the homework in class while the students still had their papers. I asked them to comment on their work, with a different writing implement than the one they used at home. 

They could correct simple mistakes, flag serious misunderstandings, tell me which problems they were worried about. I encouraged comments like "I didn't understand this at home, now I do" or even "I didn't understand this at home and I still don't".

Then I collected the papers and read and graded them. That took much less time than it would have without their comments. It also gave me better feedback about problem areas.