The incompatibility of fairness metrics refers to a fundamental challenge in machine learning and artificial intelligence: many commonly used fairness metrics cannot all be satisfied at the same time, especially when groups differ in their base rates (the underlying likelihood of an outcome). In simple terms, if you try to design an AI system that is fair according to one definition, you may be forced to violate another definition of fairness. This phenomenon is sometimes called the “impossibility theorem” for fairness metrics.
Let’s break down how this works. In AI, fairness is not a single, universal concept. There are multiple ways to define what it means for an algorithm to be fair. Some popular fairness metrics include demographic parity, equalized odds, predictive parity, and others. Each metric focuses on different aspects of fairness. For example, demographic parity requires that each group receives positive outcomes at the same rate, while equalized odds requires that error rates (such as false positives or false negatives) are the same across groups.
The problem of incompatibility becomes especially pronounced when the groups being compared have different base rates. Imagine a scenario where two groups have different rates of a certain disease, and an AI model is being used to predict who should be screened. It’s mathematically impossible for the model to simultaneously satisfy both equalized odds and predictive parity if the disease rates differ between groups. This was formally proven in a seminal 2016 paper by computer scientists, which showed that, except in rare cases when base rates are equal, achieving multiple fairness metrics at once is unattainable.
This has real-world implications. Organizations deploying AI systems must carefully choose which fairness metric aligns best with their values and the context of their application. For instance, in hiring, you might prioritize equal opportunity, while in lending you may focus on predictive parity. Whichever metric is chosen, it’s important to understand that optimizing for one can lead to trade-offs or unintended biases according to others. This makes transparency and stakeholder input crucial in the development and deployment of fair AI systems.
Understanding the incompatibility of fairness metrics helps practitioners avoid the common pitfall of assuming that “fair” AI is a straightforward goal. Instead, it’s an exercise in balancing competing values and making informed decisions about which aspects of fairness are most important for a specific use case. Researchers continue to explore new metrics and methods to either relax these trade-offs or design systems that make these trade-offs explicit.
For anyone working with AI in sensitive domains like healthcare, finance, or criminal justice, being aware of the incompatibility of fairness metrics is essential. It encourages open discussion about fairness choices and the limitations of automated decision-making, ultimately promoting more responsible and ethical AI.
