We consider problems of rating alternatives based on their pairwise comparisons according to several criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall priorities of each alternative. We offer a solution that involve the minimax approximation of the comparison matrices by a common (consistent) matrix of unit rank in terms of the Chebyshev metric in logarithmic scale. The approximation problem reduces to a multi-objective optimization problem to minimize simultaneously the approximation errors for all comparison matrices. We formulate the problem in terms of tropical (idempotent) mathematics, which focuses on the theory and applications of algebraic systems with idempotent addition. To solve the optimization problem obtained, we apply methods and results of tropical optimization to derive a Pareto optimal solution. As an illustration of the approach, we present a complete Pareto optimal solution for a general problem of rating alternatives in the case of two criteria used for comparisons.