Motivated by a radically new peer review system currently under evaluation by the National Science Foundation, we study peer review systems in which proposals are reviewed by PIs who have submitted proposals themselves. An (m,k)-selection mechanism asks each PI to review m proposals, and uses these reviews to select (at most) k proposals. We are interested in impartial mechanisms, which guarantee that the ratings given by a PI to others' proposals do not affect the likelihood of the PI's own proposal being selected. We design two impartial mechanisms that --- under different assumptions --- select a k-subset of proposals that is essentially as highly rated as the one selected by the non-impartial (abstract version of) the NSF pilot mechanism, even when the latter mechanism has the ``unfair'' advantage of eliciting honest reviews.
Joint work with David Kurokawa, Omer Lev, and Ariel Procaccia