# Fairness Analysis with Shapley-Owen Effects

arXiv: https://arxiv.org/abs/2409.19318 · HTML: https://mlsanity.com/paper/2409.19318/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Owen-Shapley Policy Optimization: A Principled RL Algorithm for Generative Search LLMs](https://mlsanity.com/paper/2601.08403/) (2026)

## Abstract (arXiv)

We argue that relative importance and its equitable attribution in terms of Shapley-Owen effects is an appropriate one, and, if we accept a small number of reasonable imperatives for equitable attribution, the only way to measure fairness. On the other hand, the computation of Shapley-Owen effects can be very demanding. Our main technical result is a spectral decomposition of the Shapley-Owen effects, which decomposes the computation of these indices into a model-specific and a model-independent part. The model-independent part is precomputed once and for all, and the model-specific computation of Shapley-Owen effects is expressed analytically in terms of the coefficients of the model's polynomial chaos expansion (PCE), which can now be reused to compute different Shapley-Owen effects. We also propose an algorithm for computing precise and sparse truncations of the PCE of the model and the spectral decomposition of the Shapley-Owen effects, together with upper bounds on the accumulated approximation errors. The approximations of both the PCE and the Shapley-Owen effects converge to their true values.