The purpose of this paper is to analyze the causes and effects of arbitrariness in the peer review process. This paper focuses on two main reasons for the arbitrariness in peer review. The first is that referees are not homogenous and display homophily in their taste and perception of innovative ideas. The second element is that reviewers are different in the time they allocate for peer review. Our model replicates the NIPS experiment of 2014, showing that the ratings of peer review are not robust, and that altering reviewers leads to a dramatic impact on the ranking of the papers. This paper also shows that innovative works are not highly ranked in the existing peer review process, and in consequence are often rejected.