October 17, 2019


Disparate Causes, pt. II

The “Path-Specific Effects” View of Discrimination

An accurate understanding of the nature of race in our society is a prerequisite for an adequate normative theory of discrimination. If, as part one of this post suggests, limiting discrimination to direct effects of race misunderstands the nature of living as a raced subject in a raced society, then perhaps the extension of the scope of discrimination to also include indirect effects of race would better approximate the social constructivist view of race.

Recent approaches to causal and counterfactual fairness seek fair decision procedures “achieved by correcting the variables that are descendants of the protected attribute along unfair pathways.”1 The method, thus, cancels out certain effects that are downstream of race in the diagram, and retains only those path-specific effects of race that are considered fair. Despite the expanded scope of what counts as a discriminatory effect, the logic of the Path-Specific Effects method follows that of the original Pearlian causal counterfactual model of discrimination: race, as a sensitive attribute, is toggled white or black atop a causal diagram, and its effect cascades down various paths leading to the outcome variable. But, this time, the causal fairness technician does more than measure and limit the direct effect of race on the final outcome; she now also measures effects of race that are mediated by other attributes, keeping only those effects carried along paths deemed “fair.”

In theory, it seems the Path-Specific Effects approach might be able to meet Kohler-Hausmann’s challenge that discrimination detection methods recognize the “real lived institutions of racial orders”—and zero them out accordingly. Suppose, for the sake of argument, that Jamal has a GPA, and that that GPA is “caused” by both his race and his knowledge of class material. It’s “caused” by his race, let’s say, because he attends a high school with an environment that is hostile to Black students, and it’s “caused” by his knowledge of class material insofar as his grades reflect evaluations of that knowledge. A Path-Specific Effects approach to modeling this situation might constrain the former “unfair” effect outlined by the path racegpacallback outcome, while retaining the “fair” effect outlined by the path knowledgegpacallback outcome (see Figure 1 below).

The same might go for effects of race that are carried forth via a longer chain of mediators, like racefamily socioeconomic statusprevious work historycallback outcome. The Path-Specific Effects approach can ensure effects along that chain are collapsed down to zero as well, leaving only fair causes and effects to exert any influence on the final decision outcome. Where the Direct Effects method incorrectly imagines race to be a surface-level trait by measuring only direct effects, the Path-Specific Effects method allows us to consider indirect effects, and thus appreciates and represents the social constructivist view of race. Voilà!

Figure 1

Let’s take stock of the two causal counterfactual approaches to racial discrimination that we’ve looked at: the Direct Effect and the Path-Specific Effects approaches. Both methods cast discrimination as a question about differential treatment of counterfactual counterparts: When we ask the paradigmatic discrimination question, “Would X who is white have been hired if X were Black?” we are asking a question about counterparts. Discrimination, in the causal counterfactual framing, happens when X-as-white gets hired, whereas counterpart-X-as-Black does not. Framed in this way, we can understand different theories of causal counterfactual fairness (or discrimination) to be presenting different proposals for what the counterpart relation between X-as-white and X-as-Black should be to ensure non-discrimination. The Direct Effect view posits that the audit study counterpart relation is sufficient: just make Greg and Jamal identical in all respects but their names and measure the difference in their callback rates. Discrimination happens, the Direct Effect account claims, when this difference is nonzero.

The Path-Specific Effects advocate works from a more sophisticated theory of how race comes to affect a person’s life. She admits that many aspects of one’s life are influenced by race prior to a particular decision, and failing to account for those aspects risks perpetrating that injustice in the present decision. An audit study following this reasoning would claim that Jamal’s counterpart is not just Greg who is white while otherwise identical to him, but some Greg whose résumé features are altered to account for the fact that on average, Greg, being white, probabilistically faced fewer obstacles than Jamal in feeling safe at school, taking the SAT, being recommended to enroll in AP English, and so on. This white Greg—call him Greg1— is Jamal’s counterpart under the Path-Specific Effects approach, and a decision process cannot treat the two differently if it is to be non-discriminatory. In addition to the standard descriptive knowledge required to construct the causal diagram, then, the Path-Specific Effects approach explicitly requires normative valuations about the fairness of certain path effects of race over others. But perhaps this is all right! After all, determinations of discrimination do require both normative and descriptive judgments. Let’s recall Kohler-Hausmann: “The ideal experiment to detect discrimination in the counterfactual causal model is one in which the researcher…. [zeroes] out the average differences in relevant variables that were produced by the real lived institutions of racial orders.”2 Perhaps this can be translated into designations of unfair pathways (those that are to be zeroed out) and fair pathways (those we can keep). If so, are determinations of discrimination reducible to causal counterfactual models after all?

On the Hunt for the Correct Counterfactual

Kohler-Hausmann’s challenge asks us to question the very attribute nodes and one-directional arrows that make up our causal diagrams. While I do not find Path-Specific Effects methods to fully respond to the challenge, the approach makes attempts at representing the socially-embedded and experience-shaping nature of race. But the critique of the methods that I venture here concerns the particular forms of reasoning about discrimination and equality that causal counterfactual methods require, and asks whether engaging such reasoning is: 1) plausible as a way of understanding discrimination as a distinct kind of moral (and legal) wrong and 2) practical as a means toward building fair decision systems.

The Path-Specific Effects methodology is complex: Combining a more robust theory of race and a normative theory of discrimination with path-specific causal inference methods requires one to draw a causal diagram that rolls together sociological causal mechanisms with normative judgments about which causes and effects ought to be considered fair. For example, we might find there to be probabilistic correlations between the age, race, and neighborhood of residence of applicants who apply for a particular job in a city, and seek to determine a causal connection. How to draw the relationship between the nodes age and race and neighborhood will depend not only on the social and historical context of the job and city (which will affect the way in which those features are causally related), but also on normative judgments of whether and in what way those features ought to be incorporated into the decision outcome. How exactly should one go about determining which effects are unfair and how inference procedures should account for this unfairness? This is the central normative task of the Path-Specific Effects approach, yet neither causal reasoning nor sheer moral intuition offer much guidance about how to proceed.

An example using the language of the counterpart relation will be instructive. To determine whether an employment callback decision process was fair, causal approaches ask us to determine the white counterpart to Jamal, a Black male who is a junior with a 3.7 GPA at the predominantly Black Pomona High School. When we toggle Jamal’s race attribute from black to white and cascade the effect to all of his “downstream” attributes, he becomes white Greg. Who is this Greg? Is it Greg of the original audit study, a white male who is a junior at Pomona High School with a 3.7 GPA? Is it Greg1, a white male who is a junior at Pomona High School with a 3.9 GPA (adjusted for the average Black-White GPA gap at Pomona High School)? Or is it Greg2, a white male who is a junior at nearby Diamond Ranch High School—the predominantly white school in the area—with a 3.82 GPA (accounting for nationwide Black-White GPA gap)? Which counterfactual determines whether Jamal has been treated fairly? Will the real white Greg please stand up?

Perhaps I’m being demanding by asking about the full description of Jamal’s counterpart from the outset. Let’s start with a simpler task: constraining the effect of Jamal’s race on his GPA as given by the causal diagram in Figure 2. That is, we want to know white Greg’s GPA.

Figure 2

To make this adjustment, should the decision process transform Jamal’s GPA according to a nationwide metric—perhaps the national Black-White GPA gap? Perhaps the school-specific GPA gap? The state-wide gap? Perhaps a metric that only measures the Black-White gap among high school juniors? To what criteria should we refer in order to decide? Referring to “causal facts” won’t get us very far—after all, each gap is as empirically rooted as any other. What can we say about which counterpart relation is fairer to Jamal? To Black job applicants generally? Does anyone actually reason about racial equality in this way? Should they?

My point is this: the constructivist view of race claims we can only understand it within a broader system of racial subordination and domination, in which being raced Black, for example, is inextricably (probabilistically) bound up with historic disadvantage, community under-resourcing, forms of state violence, and so on and so forth. If you buy this view, then it seems clear that ideas about fairness and discrimination do not come to us ex nihilo as precise judgments about permissible causal effects, troubling mediators, and ideal adjustment criteria that need only be plugged into technical machinery to generate results that are certifiably fair. Judgments about fairness and discrimination do not come to us as convictions about the “correctness” of adjusting the Black-White SAT gap by average schoolwide gap vs. average statewide gap vs. average nationwide gap. As I see it, they come to us as normative valuations about why certain observational data of decision outcomes are wrongfully racially biased. These valuations might be explained in causal terms, but they are not founded on causal reasoning. Normative assessments of observational outcomes inform the structure of our causal diagrams, not the other way around.

Here’s a good heuristic to check my claim: If unfair causal effects can be picked out and plugged into the Path-Specific Effects methodology, the resulting outcomes will, in the best case, match our normative valuations about what a fair decision procedure should be like. If they yield results we agree with, then the designation of what effects are fair and unfair will seem to have been right but in a tautological way. If they do not, then our designation of fair effects will have to be changed to accord with our moral judgments regarding the kind of equality we want to ensure. If this is right, then we might wonder what extra work causal counterfactual reasoning is doing in our understanding of discrimination and fairness.

The Upshot

The law often appears non-committal when it comes to the normative grounds on which anti-discrimination legislation stands. But algorithmic fairness methods frequently seek to do more than simply ensure that machine decisions are not legally discriminatory. Much of the field has moved to define new metrics of fairness and corresponding methods to satisfy them. Recent causal counterfactual methods in algorithmic fairness operate in that lineage of work, extending beyond the forms of justice and injustice recognized in the law. Some even explicitly aim to “break the cycle of injustice” that marginalized social groups have suffered and continue to suffer.3 Path-Specific approaches thus mark a significant advance in our theorizing about what it might take to build processes that treat fairly groups that have been historically and presently oppressed. By pointing out the conceptual and normative limitations of even these ambitious and politically salutary methods, I look toward a theory of anti-discrimination as a means toward a more substantive relational equality on the horizon.

When we ask how decision procedures can be made fair, we are not asking how to ensure correct and proper causal relationships between race, neighborhood of residence, Jamal’s other qualifications, and his final callback outcome. We are instead asking what it would require to ensure some level of equality between Jamals and Gregs in the labor market and in society more broadly. Whether ensuring such equality can eventually be cashed out procedurally in terms of some ideal counterpart relationship between Jamal and Greg is an open question. But to mistake the important question of what it takes for a decision process to be fair for a question about what causal mechanisms generate observed racial inequality, and whether those mechanisms are unfair, is to pass over a broad normative landscape of reasons we care about racial equality for the very narrow frame of ensuring procedural fairness in a causal chain.

In many cases, answering the causal question is irrelevant to answering the justice question. The gaping health disparities between white people and Black people in the U.S. is one example: Whatever health Black people “would have had” in some convoluted counterfactual scenario is frankly irrelevant to the question of whether actually existing inequality is a matter of injustice—let alone what can be done to remedy it.

In other cases, the causal question is entirely derivative of normative judgments about observational data. For example, the now infamous question of whether or not the single digit number of Black students admitted into New York City’s Stuyvesant High School is evidence of a racially unfair decision process appears to fall into this camp. In this case, independent judgments about the value and purpose of having elite public schools and the value and purpose of maintaining some racial balance in them will answer the question rather quickly. Whether those judgments can also be described in the language of causal pathways and structural equations modeling bears neither on our ability to make those judgments nor on the overall quality of those judgments.

Thinking causally about the effects of race can help inform and elucidate some of our normative judgments about what we ought to do in our efforts toward racial equality, and the specific task of drawing a causal diagram might even be productive for our public discourse. But if the goal of our causal fairness methods is to build decision procedures that are racially just, we should start by asking what type of outcomes we would expect a racially just procedure to yield. We likely won’t have a precise racial breakdown in mind, but nevertheless the outcome might turn out to be a goal we can aim for. Such an approach to fairness would require much less statistical and causal finagling on our end, but to riff on the words of Chief Justice John Roberts—I’ll ascribe them to the Chief Justice’s racially just counterpart—sometimes “the way to fix inequalities in the category of race is to fix inequalities in the category of race.”

To read the first part of this series, click here.

  1. Silvia Chiappa and Thomas Gillam. “Path-Specific Counterfactual Fairness.” AAAI. (2018): 8. 
  2. Kohler-Hausmann, Issa. “Eddie Murphy and the Dangers of Counterfactual Causal Thinking About Detecting Racial Discrimination.” (January 1, 2019): 1212. 
  3. Nabi, Razieh, Daniel Malinsky and Ilya Shpitser. “Learning Optimal Fair Policies.” ArXiv abs/1809.02244 (2018). 

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