I am glad to read this because I have been using this approach for many years with students' writing dossiers in my biology capstone course. There, my students must prepare a two-page type-written response to the day's assigned reading for entry into the class. That is a lot of pages to mark! Many years ago I attended a critical thinking conference by Richard Paul in which he advocated that it was important to encourage students to write daily to help them articulate their thinking. To encourage attention to the assignment he advised that only a portion of their writing dossier need be marked.
My tweak to this approach has been to have students identify what they consider to be their weakest and strongest piece in their writing dossier explaining why they think each is so. To reward their critical analysis of their own writing I assure students that I will mark their best but only comment (not grade) their worst provided they articulate what they think makes each strong or weak. In addition, I'll randomly choose a couple more writing pieces to grade.
It's nice to have the evidence in support of this approach to marking selections of student work.
Weimer M. 2015. Designing homework that enhances learning. The Teaching Professor 29(3): 2-3 http://www.magnapubs.com/newsletter/the-teaching-professor/111/Designing-Homework-That-Enhances-Learning-13405-1.html