Learning Social Welfare Functions

TL;DR

This paper investigates learning social welfare functions, specifically power mean functions, from decision data and pairwise comparisons, demonstrating their learnability with polynomial sample complexity and providing practical algorithms.

Contribution

It formalizes the problem of learning social welfare functions, proves their learnability with polynomial samples, and develops practical algorithms for real-world application.

Findings

Power mean functions are learnable with polynomial sample complexity.

Algorithms perform well even with noisy social welfare data.

Two learning tasks are effectively addressed: utility vectors and pairwise comparisons.

Abstract

Is it possible to understand or imitate a policy maker's rationale by looking at past decisions they made? We formalize this question as the problem of learning social welfare functions belonging to the well-studied family of power mean functions. We focus on two learning tasks; in the first, the input is vectors of utilities of an action (decision or policy) for individuals in a group and their associated social welfare as judged by a policy maker, whereas in the second, the input is pairwise comparisons between the welfares associated with a given pair of utility vectors. We show that power mean functions are learnable with polynomial sample complexity in both cases, even if the comparisons are social welfare information is noisy. Finally, we design practical algorithms for these tasks and evaluate their performance.