You seem to have the grading scheme mis-targeted.
When you make peer review part of your grading scheme you grade the review not the paper reviewed. Failure to do the review should be reflected in the reviewer's grade not in the author's grade.
The criteria I use for grading reviews are along the lines of
- Does the review correctly identify strengths and weakness of the submitted material?
- Does it communicate problems clearly and helpfully to the author?
- Are the criticisms couched in constructive language? (I know, this is not actually necessary or honored in the real world, but I want my classroom to be a comfortable learning environment so I insist.)
- Does the review identify what parts of the paper are the source of particular complaints. ("Section 3.2 is unclear because..." as opposed to "Some parts of the paper are unclear").
Note that this means I have to read and review the paper myself and then read and grade the reviews. It's painfully time-consuming.
The positive aspects of this kind of assignment is that it engages the students at the "evaluation" tier of Bloom's taxonomy, and exposes them to a range of different quality of work so they get a chance to understand for themselves that some writing is just plain better than other samples.
The negative aspects include the amount of time used, the somewhat subjective nature of the grading criteria, and a tendency for students to tell each other how very well they are all doing (it requires a certain expertise to do a good—and especially a critical—job of evaluating the work of others; if your students aren't at that level yet they won't set high standards for their peers).
Over the weekend I saw a talk on a system called calibrated peer review, which provides a framework for using peer review as part of the grading scheme for student essays. I have no personal experience with the system.
The whole system is mediated over the internet. Assignments proceed in several phases.
Student receive the prompt, do any necessary research, then write and submit their response.
Students then receive a rubric for assessing responses to the same assignment and apply it to three sample responses provided by the instructor (designed to mimic poor, adequate and good student responses).
Success in this stage is defined by having a rating close to that assigned by the instructor. They are allowed a second chance on any where they deviate excessively.
The weight of a students review in the third stage is determined by their performance in this stage (students whose use of the rubric does not match the instructor's will have less impact then student whose application of the rubric matches the instructor's).
Students then read and rate three anonymous responses from their peers (and possibly from the instructor who can provide a 'student' response as well as the three used for calibration). These responses are factored into the author's grade on the assignment using the weights established in stage 2.
Finally, students read and rate their own response. Success here defined by matching the consensus.
Disputes and special cases are resolved by the instructor.
Clearly there is a lot going on there. The anonymity, the use of the calibration stage, and the weighting of student evaluations by their success in rating the calibration responses all work to prevent the worst failure modes of just asking students to grade each other's work directly. Even so, you need that rule that the instructor can overrule the system in exceptional case.
When all is said and done a student's grade on the assignment can be based more on their rating (of samples, of their peers's responses, and of their own submission) than on their own writing. The speaker showed a grading scheme he used in which the essay itself was only worth 20% of the assignment grade with the rest coming from various parts of the review sequence.
This is a lengthy process and is used more on short writing assignment than on substantial papers. It also requires considerable prep, as the instructor must provide the prompt, the rubric, three calibration responses and possibly a fake 'student' response.