  The literature on ranking from ordinal data is vast, and there are several
ways to aggregate overall preferences from pairwise comparisons between
objects. In particular, it is well known that any Nash equilibrium of the zero
sum game induced by the preference matrix defines a natural solution concept
(winning distribution over objects) known as a von Neumann winner. Many
real-world problems, however, are inevitably multi-criteria, with different
pairwise preferences governing the different criteria. In this work, we
generalize the notion of a von Neumann winner to the multi-criteria setting by
taking inspiration from Blackwell's approachability. Our framework allows for
non-linear aggregation of preferences across criteria, and generalizes the
linearization-based approach from multi-objective optimization.
  From a theoretical standpoint, we show that the Blackwell winner of a
multi-criteria problem instance can be computed as the solution to a convex
optimization problem. Furthermore, given random samples of pairwise
comparisons, we show that a simple plug-in estimator achieves near-optimal
minimax sample complexity. Finally, we showcase the practical utility of our
framework in a user study on autonomous driving, where we find that the
Blackwell winner outperforms the von Neumann winner for the overall
preferences.
