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