Problems with open participation in peer review

In this letter, we study an open participation model of peer review in which potential reviewers choose whether to review a manuscript, at a cost, without a formal invitation. The outcome is a compromise among the reviewers' recommendations. Here we show that the equilibrium number of reviewers in the public peer review is small, their recommendations are extreme, and the outcome is likely to be random when the compromise is the median of the reviewers' recommendations.