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Proxy Discrimination After Students for Fair Admissions

This article proposes a comparative legal test for regulating proxy discrimination following *Students for Fair Admissions*, arguing that decision tools are narrowly tailored when they utilize variables with the weakest total proxy power and suggesting that lawmakers establish caps on permissible proxy power while plaintiffs bear the burden of identifying less discriminatory alternatives.

Original authors: Frank Fagan

Published 2026-04-24

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Frank Fagan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The "Ghost" in the Machine

Imagine you are a bank manager trying to decide who gets a loan. You know the law says you cannot reject someone just because of their race. So, you tell your computer, "Don't look at race!"

The computer obeys. It ignores the "Race" column. But here's the trick: The computer starts looking at Zip Codes instead.

In many cities, zip codes are heavily segregated. If you live in a specific zip code, there is a very high chance you are of a certain race. So, even though the computer isn't looking at "Race," it is looking at "Zip Code," which acts as a perfect stand-in (or a proxy) for race.

The Analogy:
Imagine a bouncer at a club who says, "I don't care what color your shirt is." But then he says, "I only let in people wearing red shoes." If everyone who wears red shoes happens to be from a specific neighborhood, the bouncer has effectively banned that neighborhood without ever mentioning it. He is using a proxy (shoe color) to do what he can't do directly (ban a neighborhood).

The Supreme Court recently ruled that colleges can't use race directly for admissions. But this paper asks: What stops colleges from using "proxies" like high school attended, parents' income, or zip code to achieve the exact same result?

The Solution: Measuring "Proxy Power"

The author, Frank Fagan, suggests we need a new way to measure how much these "proxy" variables are doing the dirty work. He calls this "Proxy Power."

Think of a recipe for a cake.

The Goal: Make a delicious cake (e.g., predict who will repay a loan or succeed in college).
The Ingredients: Variables like test scores, income, zip code, etc.
The Forbidden Ingredient: Race.

If you take "Race" out of the recipe, but you keep "Zip Code," and the cake tastes exactly the same, then Zip Code is doing the work of Race. It has high "Proxy Power."

Fagan proposes three ways to fix this:

1. The "No-Go" Zone (For Perfect Proxies)

Sometimes, a proxy is so strong it's basically the same thing as the forbidden variable.

Analogy: Imagine a rule that says, "No one with a specific genetic marker can enter." If that genetic marker is 100% linked to a specific race, using that marker is just using race in disguise.
The Rule: If a variable is a "perfect substitute" for a protected class (like race or gender), it should be banned immediately. It's like trying to sneak a banned substance into a party by hiding it in a box that is clearly labeled with the substance's name.

2. The "Best Alternative" Contest (Comparative Minimum)

This is the main idea of the paper. Often, we can't ban a variable entirely because it does help predict success (e.g., income helps predict loan repayment). But maybe there is a better way to predict success that doesn't rely on race proxies.

The Analogy: Imagine two chefs trying to make the best soup.
- Chef A uses a secret ingredient that happens to be linked to a specific ethnicity. The soup tastes great.
- Chef B uses a different set of ingredients that makes the soup taste exactly the same, but none of the ingredients are linked to ethnicity.
- The Verdict: Chef B wins. The law should force Chef A to switch to Chef B's recipe.

The Test: If two algorithms (or decision tools) predict the outcome equally well, but one uses fewer "race-linked" variables, the one with fewer proxies is the legal winner.

3. The "Speed Limit" (Capped Proxy Power)

Sometimes, it's hard to tell which recipe is better. The math is messy.

The Analogy: Imagine a speed limit sign. You don't need to calculate the exact aerodynamics of every car to know that driving 90 mph is too fast. You just set a limit: "No more than 55 mph."
The Rule: We could set a "cap" on how much proxy power is allowed. If a variable adds more than a tiny, insignificant amount of accuracy (say, 5%) but causes a huge amount of discrimination, it gets cut. It's a "speed limit" for discrimination.

Who Has to Do the Work? (The Burden of Proof)

A major question in the paper is: Who has to find the better recipe?

Current Law: The person who feels discriminated against (the Plaintiff) has to find a better way for the company to do things. This is like asking a customer to come up with a better recipe for the restaurant.
The Paper's Suggestion: This is unfair and hard. The company (the Defendant) has all the data and the computers. They should be the ones searching for a less discriminatory way.
The "Competition" Idea: The author suggests a "cooking competition."
1. The company gives the data (anonymized) to a neutral judge.
2. The Plaintiff (the accuser) builds their own algorithm using public data.
3. The Company builds their own algorithm.
4. They both try to make the best prediction.
5. The Winner: The algorithm that predicts the outcome best while using the least amount of discriminatory proxies wins.

This forces the company to be honest. If they can't beat the Plaintiff's "clean" algorithm, they have to admit their current one is too discriminatory.

The "Black Box" Problem

Finally, the paper talks about secrecy.

The Problem: Sometimes, a human committee makes decisions in a closed room. They don't write down why they rejected someone. They just say, "We felt it wasn't a good fit." This is a "Black Box."
The Fix: Even if we can't see inside the human mind, we can compare the results. If a human committee rejects 90% of older workers, but a simple, transparent computer program can achieve the same business goals while rejecting only 50%, the human committee is failing the "comparative test."

Summary: The Takeaway

The paper argues that we can't just say "Don't use race." We have to look at the whole picture.

Look for the Ghost: Check if "neutral" variables (like zip codes) are just hiding race.
Compare the Tools: If you can achieve your goal (like lending money or admitting students) with a tool that is less discriminatory, you must use that tool.
Put the Burden on the Boss: The companies and schools have the data and the power, so they should be the ones proving they aren't using "proxy" discrimination.

In short: You can't hide a banned ingredient just by changing its name. If you can make the cake taste just as good without the banned ingredient, you have to do it.

Based on the article "Proxy Discrimination After Students for Fair Admissions" by Frank Fagan, here is a detailed technical summary covering the problem, methodology, key contributions, results, and significance.

1. The Problem

The paper addresses the legal and technical challenge of proxy discrimination in the wake of the U.S. Supreme Court's ruling in Students for Fair Admissions (SFFA) v. Harvard.

The Legal Gap: While SFFA prohibits direct race-based admissions, it allows institutions to consider how race has affected an applicant's life (e.g., overcoming discrimination). However, this creates a loophole where decision-makers (universities, lenders, employers) can use facially neutral variables (proxies) that correlate highly with protected classes (race, sex, etc.) to achieve discriminatory outcomes indirectly.
The Technical Challenge: Algorithms can easily circumvent anti-discrimination laws by using proxy variables (e.g., zip code, high school attended, parental income, digital footprints) that act as statistical substitutes for protected classes.
The Core Question: Current law lacks a clear, technical test to regulate the use of these proxies. It is unclear when a proxy is permissible (as a legitimate business factor) versus when it constitutes unlawful indirect discrimination, especially when removing the proxy might slightly reduce predictive accuracy.

2. Methodology

The author employs a comparative statistical and legal framework to propose a new regulatory test. The methodology involves:

Statistical Definition of Proxies: Defining proxies not just by correlation, but by their "Total Proxy Power." This is measured by how much a protected class variable (e.g., race) explains the variation in the outcome after the model's neutral variables are accounted for.
- Perfect Substitutes: Variables that perfectly predict a protected class (e.g., a specific high school in a segregated district).
- Imperfect Substitutes: Variables with partial correlation (measured via $R^2$ or pseudo- $R^2$ in regression analysis).
Comparative Analysis: The paper proposes comparing two decision models (algorithms) that achieve the same lawful goal (e.g., predicting loan default or academic success).
- Metric: The model with the lower Total Proxy Power is deemed the "less discriminatory alternative," provided it maintains comparable predictive accuracy.
Legal Synthesis: The author integrates concepts from disparate impact theory (Title VII, Fair Housing Act, ECOA) and strict scrutiny (Equal Protection) to derive a unified standard for algorithmic fairness.

3. Key Contributions

The paper proposes three specific legal tests and a procedural framework for managing proxy discrimination:

A. The Three Legal Tests for Proxy Power

The No Proxy Rule (for Perfect Substitutes):
- If a neutral variable is a perfect (or near-perfect) substitute for a protected class, its use should be prohibited.
- Rationale: Using a variable that perfectly predicts race is statistically identical to using race itself. If other variables can achieve the same goal without this perfect substitution, the proxy is superfluous and discriminatory.
The Comparative Minimum Proxy Power Standard:
- When perfect substitutes do not exist, decision-makers must choose the algorithm that exhibits the weakest total proxy power among available alternatives that achieve the same accuracy.
- Mechanism: If Model A and Model B both predict loan defaults with 95% accuracy, but Model A has a proxy power of 0.08 (8% of variation explained by race) and Model B has 0.05, Model B must be used.
The Capped Proxy Power Rule:
- To address measurement errors and administrative costs in "close cases," the author suggests setting a statistical cap (e.g., a 5% threshold) on permissible proxy power.
- If the difference in proxy power between two models falls below the cap, the less discriminatory model is preferred. This creates a "safe harbor" for minor deviations while preventing significant indirect discrimination.

B. Addressing Unmeasured Goals

The paper argues that proxy minimization is impossible without a clearly defined objective function (e.g., "maximize loan repayment" vs. "train future leaders").
It suggests that courts should require decision-makers to articulate sufficiently measurable goals. Vague goals (like "diversity" without metrics) allow for excessive discretion and retrofitting of discriminatory proxies.

C. Burden of Production and Algorithmic Competition

Shift in Burden: The paper challenges the current legal norm where plaintiffs must find less discriminatory alternatives. It argues that while plaintiffs should bear the burden, the mechanism should be Algorithmic Competition.
The Mechanism:
1. A "lock-box" testing dataset is created (representative of the defendant's population).
2. Both the plaintiff and defendant build algorithms to achieve the stated goal.
3. The algorithm that achieves the goal with the lowest proxy power wins.
Significance: This incentivizes defendants to search for better models and prevents them from hiding behind "black box" algorithms or opaque human committees.

4. Results and Findings

Feasibility of Measurement: The author demonstrates that proxy power can be quantified using standard statistical techniques (e.g., calculating the incremental $R^2$ when a protected class variable is added to a model).
Trade-off Resolution: The paper resolves the tension between accuracy and fairness. If a less discriminatory alternative exists with comparable accuracy, the discriminatory proxy must be removed.
Handling "Business Necessity": The paper refines the "business necessity" defense. A business need (e.g., profit maximization) does not justify high proxy power if a model with lower proxy power can achieve the same profit level.
Retrofitting Prevention: The paper identifies a risk where institutions might "retrofit" a low-proxy explanation for a discriminatory decision after the fact. It suggests pre-commitment (announcing algorithms before data collection) or limiting the number of variables to prevent this.

5. Significance

Post-SFFA Legal Framework: The article provides a concrete legal test for courts to apply in the post-SFFA era, moving beyond the vague prohibition of "race" to a rigorous analysis of indirect discrimination via proxies.
Algorithmic Accountability: It offers a practical, technical solution for regulating AI and machine learning in high-stakes domains (finance, hiring, education) without banning them outright.
Economic Efficiency: By framing the issue as a minimization of social costs (discrimination) while maintaining private goals (profit/academic success), the paper aligns legal requirements with economic efficiency.
Procedural Innovation: The proposal of Algorithmic Competition transforms the litigation process from a static review of evidence into a dynamic contest, ensuring that the "least discriminatory" method is actively discovered and implemented.

In summary, Fagan argues that the law must evolve from prohibiting direct discrimination to minimizing total proxy power through comparative analysis, statistical caps, and competitive algorithm testing, ensuring that decision-making tools are narrowly tailored to their goals without relying on protected-class substitutes.