# Closed-Loop View of the Regulation of AI: Equal Impact across Repeated Interactions

arXiv: https://arxiv.org/abs/2209.01410 · HTML: https://mlsanity.com/paper/2209.01410/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 3 Sep 2022.

## Builds on (most cited first, 21 of 21)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [AI Fairness 360: An Extensible Toolkit for Detecting, Understanding, and Mitigating Unwanted Algorithmic Bias](https://mlsanity.com/paper/1810.01943/) (2018)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [On the Apparent Conflict Between Individual and Group Fairness](https://mlsanity.com/paper/1912.06883/) (2019)
- [Demystifying the Draft EU Artificial Intelligence Act](https://mlsanity.com/paper/2107.03721/) (2021)
- [Post-processing for Individual Fairness](https://mlsanity.com/paper/2110.13796/) (2021)
- [Algorithms for Fairness in Sequential Decision Making](https://mlsanity.com/paper/1901.08568/) (2019)
- [Robust Counterfactual Explanations for Tree-Based Ensembles](https://mlsanity.com/paper/2207.02739/) (2022)
- [Hard Choices in Artificial Intelligence](https://mlsanity.com/paper/2106.11022/) (2021)
- [Toward Fairness in AI for People with Disabilities: A Research Roadmap](https://mlsanity.com/paper/1907.02227/) (2019)
- [Beyond Individual and Group Fairness](https://mlsanity.com/paper/2008.09490/) (2020)
- [Security and privacy for 6G: A survey on prospective technologies and challenges](https://mlsanity.com/paper/2108.11861/) (2021)
- [Defining the scope of AI regulations](https://mlsanity.com/paper/1909.01095/) (2019)
- [Fairness in Agreement With European Values: An Interdisciplinary Perspective on AI Regulation](https://mlsanity.com/paper/2207.01510/) (2022)
- [On the Ergodic Control of Ensembles](https://mlsanity.com/paper/1807.03256/) (2018)
- [Predictability and Fairness in Load Aggregation and Operations of Virtual Power Plants](https://mlsanity.com/paper/2110.03001/) (2021)
- [On the Ergodic Control of Ensembles in the Presence of Non-linear Filters](https://mlsanity.com/paper/2112.06767/) (2021)

## Built on by (most cited first, 3 of 3)

- [humancompatible.interconnect: Testing Properties of Repeated Uses of Interconnections of AI Systems](https://mlsanity.com/paper/2507.09626/) (2025)
- [Stochastic Sample Approximations of (Local) Moduli of Continuity](https://mlsanity.com/paper/2509.15368/) (2025)
- [humancompatible.detect: a Python Toolkit for Detecting Bias in AI Models](https://mlsanity.com/paper/2509.24340/) (2025)

## Abstract (arXiv)

There has been much recent interest in the regulation of AI. We argue for a view based on civil-rights legislation, built on the notions of equal treatment and equal impact. In a closed-loop view of the AI system and its users, the equal treatment concerns one pass through the loop. Equal impact, in our view, concerns the long-run average behaviour across repeated interactions. In order to establish the existence of the average and its properties, one needs to study the ergodic properties of the closed-loop and its unique stationary measure.