# Masking Causality and Conditional Dependence

arXiv: https://arxiv.org/abs/2603.06984 · HTML: https://mlsanity.com/paper/2603.06984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Fair Inference On Outcomes](https://mlsanity.com/paper/1705.10378/) (2017)
- [The Measure and Mismeasure of Fairness](https://mlsanity.com/paper/1808.00023/) (2018)
- [Learning Optimal Fair Policies](https://mlsanity.com/paper/1809.02244/) (2018)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Counterfactual harm](https://mlsanity.com/paper/2204.12993/) (2022)
- [Principal Fairness for Human and Algorithmic Decision-Making](https://mlsanity.com/paper/2005.10400/) (2020)
- [What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatment](https://mlsanity.com/paper/2205.10327/) (2022)
- [Randomization Inference for Treatment Effect Variation](https://mlsanity.com/paper/1412.5000/) (2014)
- [On the Hardness of Conditional Independence Testing In Practice](https://mlsanity.com/paper/2512.14000/) (2025)
- [Synthetic Potential Outcomes and Causal Mixture Identifiability](https://mlsanity.com/paper/2405.19225/) (2024)
- [Information Leakage Games: Exploring Information as a Utility Function](https://mlsanity.com/paper/2012.12060/) (2020)

## Abstract (arXiv)

Many regulatory and analytic problems require that a prohibited variable influence a decision only through a designated allowable channel -- a conditional-independence requirement that arises in path-specific fairness, the handling of classified information, and the regulation of trading on non-public information, among other settings. Such requirements may be enforced either stratum-by-stratum or, more commonly (and more efficiently), through a single averaged constraint on the conditional effect. We study the resulting enforcement problem from two perspectives. From the regulator's side, we formulate causal masking as a linear program and show that averaged-constraint optimization almost surely produces policies that violate the stratum-wise requirement while satisfying the averaged one exactly. The gains from masking grow with confounding and outcome heterogeneity, and detection requires precisely the conditional-independence tests that average constraints aim to avoid. From the optimizer's side, the same construction shows that masked policies recover most of the reward of unconstrained exploitation while being far harder to detect, making them attractive in any setting where the basis of decisions is itself sensitive. Together, these results argue that regulating direct dependence through averaged statistics on observed decisions is structurally limited, and that meaningful enforcement must operate at the level of the decision rule itself.