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Admittedly, peer grading is not the same as grading by an expert who really knows the material. But it is better than nothing! In fact, done conscientiously, using a well designed rubric, it's a lot better than you might think, particularly when the results are compared with grading by an instructor who has a large number of assignments to grade in a limited amount of time! In some studies, students were observed to learn better when they were asked to actively assess their answers and those of their peers according to the instructor's rubric. In particular, students who self-graded using a rubric outperformed students who were graded by instructors.

Loving this question for all the math reasons, but I'm also pretty psyched about the idea of using scratch-off stickers!