# Preference learning along multiple criteria: A game-theoretic perspective

Source: [Preference learning along multiple criteria: A game-theoretic perspective](<https://www.sota2.com/research/paper/68fa69eb1e209131cea24e67>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-01-04T05:04:46.148Z

Authors: Kush Bhatia, Ashwin Pananjady, Peter L. Bartlett, Anca D. Dragan, Martin J. Wainwright

Published: 2021-05-05T03:23:11.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Preference Evaluation on Mturk user study Overall Preferences 1.0](<https://www.sota2.com/research/sota/preference-evaluation-on-mturk-user-study-overall-preferences-1-0.md>): Preference Evaluation; Mturk user study Overall Preferences 1.0; Overall Preference Fraction: 76.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2105.01850>)

[PDF](<https://arxiv.org/pdf/2105.01850.pdf>)