Why AI’s Theoretical Inconsistencies Are Actually a Good Thing

In the quest to build Responsible AI (RAI) systems, researchers and practitioners often grapple with a fundamental challenge: the theoretical inconsistency of RAI metrics. Definitions of fairness, privacy, and neutrality frequently clash, creating what seems like an insurmountable roadblock. But what if these inconsistencies aren’t bugs to be fixed—but features to be embraced? A new position paper by Gordon Dai and Yunze Xiao argues just that, proposing that navigating these contradictions can lead to more robust, inclusive, and ethically sound AI systems.

The Problem of Inconsistent Metrics

RAI relies on metrics to quantify abstract ethical principles into actionable benchmarks. Fairness, for example, might be measured using demographic parity, equalized odds, or counterfactual fairness. Privacy could be evaluated via ε-differential privacy, while robustness might involve adversarial risk or calibration error. The trouble is, many of these metrics are mathematically incompatible. Classical impossibility theorems show that no single model can satisfy multiple fairness definitions simultaneously—unless it achieves perfect prediction or operates under highly unrealistic conditions.

Traditionally, the response has been to treat these inconsistencies as flaws. Researchers either pick a single "correct" metric or derive constraints to enforce consistency. But Dai and Xiao take a radically different stance: theoretical inconsistency is a feature, not a flaw. They argue that preserving and navigating these contradictions yields three key benefits:

1. Normative Pluralism: Different metrics encode different moral stances. By maintaining a suite of potentially conflicting metrics, we ensure that diverse stakeholder values are represented.
2. Epistemological Completeness: Complex ethical concepts like fairness or neutrality can’t be fully captured by a single metric. Multiple, sometimes conflicting, definitions preserve more of the underlying concept’s richness.
3. Implicit Regularization: Optimizing for conflicting objectives discourages overfitting to any one metric, leading to models that generalize better in real-world scenarios.

Case Studies in Inconsistency

The paper examines several real-world examples where theoretical inconsistencies dissolve into practical tradeoffs:

• Fairness: While no model can perfectly satisfy all fairness metrics at once, approximate fairness is often achievable. Empirical studies show that carefully engineered models can minimize disparities across multiple fairness definitions without catastrophic tradeoffs.
• Political Neutrality: AI systems can’t be perfectly neutral, but they can approximate neutrality through techniques like refusal, avoidance, or reflective neutrality. Each approach involves tradeoffs between utility, safety, and fairness.
• Accuracy vs. Privacy: Differential privacy imposes a theoretical cost on model accuracy, but in practice, models can often achieve strong privacy guarantees with minimal performance degradation.

The Value of Embracing Contradiction

Rather than forcing consistency, the authors advocate for a shift in RAI research and practice:

• Define Acceptable Inconsistency Thresholds: Instead of demanding perfect alignment, specify how much divergence between metrics is ethically and practically tolerable.
• Document Normative Assumptions: Every metric reflects specific values and tradeoffs. Transparent documentation (e.g., "Metric Provenance Sheets") can help stakeholders understand and negotiate these choices.
• Test Human-Metric Interaction: Involve end-users, domain experts, and regulators in selecting and weighting metrics. Participatory methods can reveal which tradeoffs are most acceptable in practice.

A New Research Agenda

The paper concludes with a call to action: instead of trying to eliminate inconsistency, the field should focus on characterizing acceptable inconsistency. This means:

• Developing theories that explain why approximate consistency works in practice (e.g., the Rashomon set framework).
• Building tools to help practitioners navigate tradeoffs between conflicting objectives.
• Designing evaluation dashboards that make pluralistic metrics interpretable to stakeholders.

In a world where AI systems must serve diverse populations with competing values, embracing contradiction isn’t just pragmatic—it’s essential. As Dai and Xiao put it: "The road to responsible AI requires systems that can hold multiple truths simultaneously."