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In this paper, we present a mathematical model to capture various factorswhich may influence the accuracy of a competitive group recommendation system.We apply this model to peer review systems, i.e., conference or research grantsreview, which is an essential component in our scientific community. We explorenumber of important questions, i.e., how will the number of reviews per paperaffect the accuracy of the overall recommendation? Will the score aggregationpolicy influence the final recommendation? How reviewers' preference may affectthe accuracy of the final recommendation? To answer these important questions,we formally analyze our model. Through this analysis, we obtain the insight onhow to design a randomized algorithm which is both computationally efficientand asymptotically accurate in evaluating the accuracy of a competitive grouprecommendation system. We obtain number of interesting observations: i.e., fora medium tier conference, three reviews per paper is sufficient for a highaccuracy recommendation. For prestigious conferences, one may need at leastseven reviews per paper to achieve high accuracy. We also propose aheterogeneous review strategy which requires equal or less reviewing workload,but can improve over a homogeneous review strategy in recommendation accuracyby as much as 30% . We believe our models and methodology are importantbuilding blocks to study competitive group recommendation systems.

Mathematical Modeling of Competitive Group Recommendation Systems with Application to Peer Review Systems