Automated decision making refers to the process of making decisions by technological means, like algorithms or AI. Automated decision systems are widely used in our society: from assisting doctors with medical diagnosis to screening job applications for HR-teams. These systems are often designed to optimize performance from a decision maker point of view, which can occur at the price of fairness towards individuals subjected to those decision systems. Systems that systematically disadvantage individuals belonging to a social salient group, that is defined based on shared protected characteristics like gender or ethnicity, can potentially be marked as discriminatory.
In our paper we address this tension by characterizing decision systems that are Pareto-optimal with respect to performance and fairness (i.e. decision systems that yield a maximum level of fairness for a given level of performance and vice versa). We show that decision systems on this so-called Pareto frontier always consist of group dependent threshold rules on the individual success probabilities.
Fairness as a multi-objective optimization problem
Over the past decade scholars have developed a broad range of fairness metrics to examine potential harms of algorithms on humans subjected to decisions of these algorithms. Examples of fairness metrics are selection rate, false/true negative/positive rate, etc. Some of these criteria are mathematically incompatible, meaning that they cannot even be met at the same time.
Initially, optimality theorems focussed on optimizing decision algorithms under the constraint that a selected fairness criterion is met (so-called egalitarian fairness). However, sometimes complete fairness is not possible or required; for example, a decision maker could require a certain level of performance for his decision system. In legal terms this is called a legitimate aim for some level of disparity.
Therefore, we follow a recent line of work that formulates algorithmic fairness as a multi-objective optimization problem. We include solutions that satisfy fairness only partially. This allows us to focus on the trade-offs between performance and fairness.
Characterizing the Pareto frontier
We provide a mathematical proof that shows that decision systems that are Pareto-optimal with respect to performance and fairness always take the form of group-dependent threshold rules. I.e., a Pareto optimal decision rule applies a different acceptance criterium for individuals belonging to group 1 than for individuals belonging to group 2, where the two groups are defined based on a shared protected characteristic (for example age, ethnicity or gender).
Depending on the selected fairness criterion, these Pareto optimal decision rules can be both lower-bound threshold (where all individuals that have a success probability above a given threshold are selected) or upper-bound threshold rules (where all individuals that have a success probability lower than a certain threshold are selected). This latter result seems counterintuitive as less qualified individuals are preferred over more qualified individuals. However, other scholars have already observed this behaviour, that is also known as ‘cherry-picking’, for a specific fairness criterion.
Technology-agnostic benchmark
Our findings are technology-agnostic: meaning that any decision algorithm that is trained for optimizing both performance and fairness, independent whether this is done via a simple machine learning algorithm or an opaque black-box algorithm, will adapt these group-dependent threshold rules.
In fact, we show that the decision rules on the Pareto frontier of a popular fairness enhancing algorithm (PF-SMG algorithm) are group-dependent threshold rules. This algorithm is a so-called black-box algorithm, of which it is unclear how decisions are made exactly. Since the algorithm has no access to the protected characteristic, it should in theory not be able to adapt group-dependent decision rules. However, in practice it turns out that it uses other datapoints that form proxies for this protected characteristic.
Model developers can use this knowledge to assess how far their designed model is from a Pareto-optimal model.
Legal implications
Our results also help in dealing with an important legal question. In discrimination law the so-called proportionality test is used to determine whether disparate treatment of individuals belonging to different groups is justified or not, in which case it is marked as discrimination. A part of this proportionality test is the questions whether the same objective (in this case level of DM performance) can be reached with a higher level of fairness. This question can be answered by knowing the exact location of the Pareto frontier.
This result opens the legal debate around indirect discrimination by opaque algorithms versus direct discrimination by group specific decision rules.
For technical details and citations, see the full FAccT 2026 paper:
Fairness vs Performance: Characterizing the Pareto Frontier of Algorithmic Decision Systems (Preprint, May 11, 2026)
