We propose the PeerRank method for peer assessment. This constructs a grade for an agent based on the grades proposed by the agents evaluating the agent. Since the grade of an agent is a measure of their ability to grade correctly, the PeerRank method weights grades by the grades of the grading agent. The PeerRank method also provides an incentive for agents to grade correctly. As the grades of an agent depend on the grades of the grading agents, and as these grades themselves depend on the grades of other agents, we define the PeerRank method by a fixed point equation similar to the PageRank method for ranking web-pages. We identify some formal properties of the PeerRank method (for example, it satisfies axioms of unanimity, no dummy, no discrimination and symmetry), discuss some examples, compare with related work and evaluate the performance on some synthetic data. Our results show considerable promise, reducing the error in grade predictions by a factor of 2 or more in many cases over the natural baseline of averaging peer grades.
There are a number of closely related problems to ours in the social choice literature. For example, Holzman and Moulin have studied a related problem in which a set of agents wish to select one amongst them to receive a prize @cite_2 . A fundamental assumption of this work is that nominations are impartial: your message never influences whether you win the prize. In our setting, such an assumption is less appropriate. We want your evaluation of the work of another agent to influence your evaluation. There are several reasons behind this change. First, your ability to evaluate the work of other agents measures in part your command of the subject being examined. Second, you will be incentivized to grade accurately by a better final grade. If your message cannot influence your evaluation, then you have no incentive to provide good evaluations. For this reason, even if we extend the sort of methods proposed by Holzman and Moulin to the task of ranking, the starting assumptions are very different.
@cite_2
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We study the problem of selecting a member of a set of agents based on impartial nominations by agents from that set. The problem was studied previously by and by Holzman and Moulin and has important applications in situations where representatives are selected from within a group or where publishing or funding decisions are made based on a process of peer review. Our main result concerns a randomized mechanism that in expectation selects an agent with at least half the maximum number of nominations. Subject to impartiality, this is best possible.