Labels, Proxies, and Historical Decision Bias

Construct, operationalization, observation process, prior intervention, action alignment. The gap between what an organization cares about and the column it trains on opens at the second step. A second gap opens at the fourth, and that one has a name.

Picture a courtroom. A judge decides whether to release a defendant on bail. Whether that defendant then fails to return for their court appearance is recorded — but only for the ones released. That is the selective labels problem, named and formalised by Lakkaraju and four co-authors in 2017. The courtroom is in their abstract: "For instance, in the context of judicial bail decisions, we observe the outcome of whether a defendant fails to return for their court appearance only if the human judge decides to release the defendant on bail."

The fourth box exists to flag the consequence. Where a human decision gates whether an outcome is ever observed, comparing human and machine performance on the recorded cases produces erroneous estimates. The authors do not answer that with counterfactual inference. They propose a contraction method, which exploits the fact that human decision-makers disagree with one another. The defendants the judge held never enter the data. They never leave the problem either.

A label is an operational measurement or decision outcome, not automatically ground truth. Proxy targets can encode access, enforcement, institutional priorities, and prior discrimination while remaining easy to predict. Predictive accuracy cannot validate a target that measures the wrong thing.

The point is not new, and it is not only technical. Discrimination can enter at the first step of data mining, before any model is fitted, in the definition of the target variable and the class labels. Barocas and Selbst made that argument in the California Law Review in 2016. Creditworthiness, "a good employee" — these sound like pre-existing facts about people. They are artifacts of the problem definition. Target-variable definitions, the authors write, "simply inherit the formalizations involved in preexisting assessment mechanisms".

Label review is therefore an inquiry into a decision somebody made. Who defined the construct. How outcomes become observable. Which decisions intervene before observation. Who remains unlabeled. And whether the target supports the intended action.

An outcome label records a real event — a hospitalization, a repayment. It can be concrete and reproducible. It can also arrive late, be censored, or still be shaped by access and policy. A human judgment label, such as an interview rating, captures an assessor's classification. It is rich in context, exposed to inconsistent standards and stereotypes, and in need of guidance and agreement analysis. A proxy label uses an observable substitute for a hidden construct — spending standing in for health need. It is often easier to collect. Its validity depends on mechanism and context, and it can encode structural inequality.

Proxy failure is not confined to health care. In 2016 Lum and Isaac ran a reimplementation of the PredPol algorithm over Oakland Police Department records of drug crimes for 2011, and published what came out in Significance. The locations the algorithm flagged were the neighbourhoods already over-represented in those records. In their words, "black people would be targeted by predictive policing at roughly twice the rate of whites". The 2011 National Survey on Drug Use and Health put drug use at roughly equivalent levels across racial classifications.

Recorded arrests were the available column. Crime was the construct. The distance between the two is the whole finding.

Describe the construct without using the field name. A team that struggles with that first step has usually inherited the label and every assumption attached to it. Then trace label production: access, observation, human decisions, timing, missing cases. Then test validity. Then examine how disagreement and proxy failure are distributed across groups and contexts. Then align the action, confirming that predicting the target supports a legitimate intervention.

The third step has machinery behind it. Some constructs cannot be observed at all — socioeconomic status, teacher effectiveness, risk of recidivism. Each has to be operationalised through a measurement model, and every measurement model rests on assumptions. Jacobs and Wallach brought that apparatus across from the quantitative social sciences into fairness work in 2021. What they supply is a way to test the assumptions: construct reliability and construct validity as things a team can check, rather than adjectives a team applies to its own target.

Their abstract says what goes wrong when nobody checks: "This process, which necessarily involves making assumptions, introduces the potential for mismatches between the theoretical understanding of the construct purported to be measured and its operationalization. We argue that many of the harms discussed in the literature on fairness in computational systems are direct results of such mismatches."

Not a bug in the model. A mismatch in the definition.

Label genealogy takes an afternoon. It answers what a model card rarely does: who created this column, under which policy, and for what. Expect to recover a negotiation rather than a decision.

That expectation comes from six months inside a corporate data science team, watching how a problem actually gets specified. Passi and Barocas reported the fieldwork in 2019. The choice of target variables and proxies, they found, is always negotiated and elastic, and rarely worked out with explicit normative considerations in mind. Their abstract puts the consequence to anyone reviewing a model: "Whether we consider a data science project fair often has as much to do with the formulation of the problem as any property of the resulting model."

A badly chosen target has already drawn a regulatory response, not only academic criticism. The Science paper appeared on 25 October 2019. Two New York regulators wrote to UnitedHealth Group the same day. Their subject was Optum's data analytics program Impact Pro. What they objected to was the variable it predicts: past health spending. Not the model's code.

A perfect prediction of the wrong target is still the wrong system. That is why the review ends by asking what the prediction is for. The health algorithm was accurate — accurate about health care costs. That accuracy carried a 26.3% chronic-illness gap at the 97th percentile of risk score into an enrolment decision, for a class of tools reaching roughly 200 million people in the United States each year. Accuracy was the delivery mechanism.

Record which validity failures force the team to redesign, restrict, remedy, or retire the system. The Impact Pro demand of 25 October 2019 came down to two of those four, and no third option: demonstrate the algorithm is not racially discriminatory, or cease using it.