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Counterfactual Fairness Is Not Demographic Parity, and Other Observations

Ricardo Silva

TL;DR

This note clarifies that counterfactual fairness (CF) is not generally equivalent to demographic parity (DP); CF sits on Pearl’s causal ladder as an individual fairness notion, while DP is a purely probabilistic, group-level criterion. It shows that DP does not imply CF and CF does not imply DP, even under seemingly favorable conditions, using both constructive counterexamples and analysis of prior work. The author reframes CF as an information-filtering (information bottleneck) procedure that selects which information from $X$ to use for prediction, independent of the loss function or downstream constraints, and stresses that path-specific variants and identifiability issues matter. The discussion also separates common misunderstandings about notational conventions, ancestral closure, and the role CF plays in fairness, highlighting the need for careful causal modeling in fairness research with practical implications for algorithm design. Overall, the paper urges cautious interpretation of claimed equivalences and clarifies the proper scope and purpose of CF within causal fairness frameworks.

Abstract

Blanket statements of equivalence between causal concepts and purely probabilistic concepts should be approached with care. In this short note, I examine a recent claim that counterfactual fairness is equivalent to demographic parity. The claim fails to hold up upon closer examination. I will take the opportunity to address some broader misunderstandings about counterfactual fairness.

Counterfactual Fairness Is Not Demographic Parity, and Other Observations

TL;DR

This note clarifies that counterfactual fairness (CF) is not generally equivalent to demographic parity (DP); CF sits on Pearl’s causal ladder as an individual fairness notion, while DP is a purely probabilistic, group-level criterion. It shows that DP does not imply CF and CF does not imply DP, even under seemingly favorable conditions, using both constructive counterexamples and analysis of prior work. The author reframes CF as an information-filtering (information bottleneck) procedure that selects which information from to use for prediction, independent of the loss function or downstream constraints, and stresses that path-specific variants and identifiability issues matter. The discussion also separates common misunderstandings about notational conventions, ancestral closure, and the role CF plays in fairness, highlighting the need for careful causal modeling in fairness research with practical implications for algorithm design. Overall, the paper urges cautious interpretation of claimed equivalences and clarifies the proper scope and purpose of CF within causal fairness frameworks.

Abstract

Blanket statements of equivalence between causal concepts and purely probabilistic concepts should be approached with care. In this short note, I examine a recent claim that counterfactual fairness is equivalent to demographic parity. The claim fails to hold up upon closer examination. I will take the opportunity to address some broader misunderstandings about counterfactual fairness.
Paper Structure (17 sections, 9 equations, 2 figures)

This paper contains 17 sections, 9 equations, 2 figures.

Table of Contents

  1. Introduction
  2. On Counterfactual Fairness and Demographic Parity
  3. Links between counterfactual fairness and demographic parity have been known from the beginning.
  4. Counterfactual fairness does not imply demographic parity.
  5. Demographic parity does not imply counterfactual fairness.
  6. Remarks.
  7. Comments on Rosenblatt and Witter (2023)
  8. Counterfactual fairness as a variable selection procedure.
  9. Counterfactual fairness is agnostic to loss functions and other constraints.
  10. Comments on Fawkes, Evans and Sejdinovic (2022)
  11. Ancestral closure of protected attributes was never a fundamental property of counterfactual fairness.
  12. What is counterfactual fairness for, after all?
  13. Comments on Plecko and Bareinboim (2022)
  14. Pearl's "notational confusion".
  15. Is counterfactual fairness an individual fairness notion? Yes.
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Three different acyclic directed mixed graphs encoding causal assumptions among protected attributes $A$, post-treatment variables $X$, pre-treatment variables $X_\prec$, and (latent) structural errors $U$. Variables ommitted where unnecessary/unavailable. The causal structures are augmented with the factor relating which variables are used in some predictor $\hat{Y}$, so that the Markovian structure of the system and predictor can be jointly read-off. Only (a) structurally implies demographic parity. The converse is not true even when $A$ is ignorable: an arbitrary predictor $\hat{Y}$ that satisfies demographic parity will in general not imply counterfactual fairness, as explained in the text.
  • Figure 2: How stable is the rank of a (invertible function of a) predictor based on linear regression compared to the rank of the true outcome? Poor, as expected: the law school dataset has relatively low signal-to-noise ratio. Each plot above is generated using a different subset of 40 test points. There are 40 columns of points in each plot, sorted from left to right based on the value of the final row, "True", which is the corresponding true first year average. Between any two consecutive rows, we link points which have the same corresponding rank statistic as given by a dataset of four predictors sorted by the true first year average. Listing 2T is an invertible "fair" mapping of the "unfair" true value, and Listing 2F is an invertible "fair" mapping of the "unfair" linear regression prediction. The rank correlation between "fair" linear regression and "fair" true labels is relatively weak, casting doubt about the value added of shadowing any particular $\bar{Y}$.