Exclusion of self evaluations in peer ratings: Monotonicity versus unanimity on finitely restricted domains

We consider the model of peer ratings, where each candidate is requested to evaluate all the other candidates, and an aggregation rule specifies the final score of each candidate for every possible configuration of evaluations. We show that if the candidates can select the evaluation marks from a finite and large set of real numbers, there is no aggregation rule that satisfies Monotonicity and Unanimity. We then prove that if the candidates can select the evaluation marks from a finite and small set of real numbers, the summation rule satisfies Monotonicity and Unanimity. Moreover, alternative definitions of unanimity appropriate for the model of peer ratings are proposed and discussed.