Eliciting Socially Optimal Rankings from Unfair Jurors

A jury must provide a ranking of contestants (students applying for scholarships or Ph. D. programs, gymnasts in a competition, etc.). There exists a true ranking which is common knowledge among the jurors, but it is not verifiable. The socially optimal rule is that the contestants be ranked according to the true ranking. The jurors are not impartial and, for example, may have friends (contestants that they would like to benefit) and enemies (contestants that they would like to prejudice). We study necessary and sufficient conditions on the jury under which the socially optimal rule is Nash implementable. We also propose a simple mechanism that Nash implements the socially optimal rule under these conditions.