In peer selection a group of agents must choose a subset of themselves, as winners for, e.g., peer-reviewed grants or prizes. We take a Condorcet view of this aggregation problem, assuming that there is an objective ground-truth ordering over the agents. We study agents that have a noisy perception of this ground truth and give assessments that, even when truthful, can be inaccurate. Our goal is to select the best set of agents according to the underlying ground truth by looking at the potentially unreliable assessments of the peers. Besides being potentially unreliable, we also allow agents to be self-interested, attempting to influence the outcome of the decision in their favour. Hence, we are focused on tackling the problem of impartial (or strategyproof) peer selection -- how do we prevent agents from manipulating their reviews while still selecting the most deserving individuals, all in the presence of noisy evaluations?
We propose a novel impartial peer selection algorithm, PeerNomination, that aims to fulfil the above desiderata. We provide a comprehensive theoretical analysis of the recall of PeerNomination and prove various properties, including impartiality and monotonicity. We also provide empirical results based on computer simulations to show its effectiveness compared to the state-of-the-art impartial peer selection algorithms. We then investigate the robustness of PeerNomination to various levels of noise in the reviews. In order to maintain good performance under such conditions, we extend PeerNomination by using weights for reviewers which, informally, capture some notion of reliability of the reviewer. We show, theoretically, that the new algorithm preserves strategyproofness and, empirically, that the weights help identify the noisy reviewers and hence to increase selection performance
