# Learning Social Welfare Functions

arXiv: https://arxiv.org/abs/2405.17700 · HTML: https://mlsanity.com/paper/2405.17700/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 5 of 5)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning](https://mlsanity.com/paper/2104.14504/) (2021)
- [Learning Aggregation Functions](https://mlsanity.com/paper/2012.08482/) (2020)
- [Markets Beyond Nash Welfare for Leontief Utilities](https://mlsanity.com/paper/1807.05293/) (2018)

## Built on by (most cited first, 7 of 7)

- [Projection Optimization: A General Framework for Multi-Objective and Multi-Group RLHF](https://mlsanity.com/paper/2502.15145/) (2025)
- [Societal Alignment Frameworks Can Improve LLM Alignment](https://mlsanity.com/paper/2503.00069/) (2025)
- [Navigating the Social Welfare Frontier: Portfolios for Multi-objective Reinforcement Learning](https://mlsanity.com/paper/2502.09724/) (2025)
- [Adaptive Pluralistic Alignment: A pipeline for dynamic artificial democracy](https://mlsanity.com/paper/2605.01642/) (2026)
- [AI Alignment From Social Choice Perspectives](https://mlsanity.com/paper/2606.21550/) (2026)
- [Online Social Welfare Function-based Resource Allocation](https://mlsanity.com/paper/2602.01400/) (2026)
- [When to Ask a Question: Understanding Communication Strategies in Generative AI Tools](https://mlsanity.com/paper/2605.11240/) (2026)

## Abstract (arXiv)

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.