One Model Many Scores: Using Multiverse Analysis to Prevent Fairness Hacking and Evaluate the Influence of Model Design Decisions

TL;DR

This work tackles the problem that algorithmic fairness depends on many design and evaluation decisions that are often implicit and potentially manipulable. It introduces a multiverse analysis framework for algorithmic fairness, enabling explicit enumeration of decision universes and robust assessment of how design choices affect fairness and performance, illustrated by a case study on public health coverage prediction. Key contributions include adapting multiverse analysis to ML fairness, identifying dominant decision drivers (notably train-test stratification and evaluation cutoffs) and their interactions, and demonstrating the risk of fairness hacking via evaluation strategies while providing a reproducible software stack. The method supports more transparent, robust, and ethically informed deployment of ADM systems by exposing the distribution of fairness outcomes rather than a single metric, thus guiding stakeholders toward safer and fairer design choices.

Abstract

A vast number of systems across the world use algorithmic decision making (ADM) to (partially) automate decisions that have previously been made by humans. The downstream effects of ADM systems critically depend on the decisions made during a systems' design, implementation, and evaluation, as biases in data can be mitigated or reinforced along the modeling pipeline. Many of these decisions are made implicitly, without knowing exactly how they will influence the final system. To study this issue, we draw on insights from the field of psychology and introduce the method of multiverse analysis for algorithmic fairness. In our proposed method, we turn implicit decisions during design and evaluation into explicit ones and demonstrate their fairness implications. By combining decisions, we create a grid of all possible "universes" of decision combinations. For each of these universes, we compute metrics of fairness and performance. Using the resulting dataset, one can investigate the variability and robustness of fairness scores and see how and which decisions impact fairness. We demonstrate how multiverse analyses can be used to better understand fairness implications of design and evaluation decisions using an exemplary case study of predicting public health care coverage for vulnerable populations. Our results highlight how decisions regarding the evaluation of a system can lead to vastly different fairness metrics for the same model. This is problematic, as a nefarious actor could optimise or "hack" a fairness metric to portray a discriminating model as fair merely by changing how it is evaluated. We illustrate how a multiverse analysis can help to address this issue.

Figures (11)

• Figure 1: Steps to conduct a multiverse analysis for algorithmic fairness. Steps 1 - 4 apply to multiverse analyses in general, whereas steps 5 - 6 are unique to larger multiverse analyses for algorithmic fairness.
• Figure 2: Variation in the multiverse spans the entirety of possible values of the fairness metric. Distribution of fairness metric (equalized odds difference) across universes. Lower values on the fairness metric indicate smaller TPR and FPR differences across groups.
• Figure 3: Performance and fairness are largely unrelated with plateaus of low variance in performance, but high variance in fairness. Distribution of overall performance as $F_{1}$ score and fairness metric (equalized odds difference) across all multiverses. Marginal histogram shows distribution of performance. A marginal histogram of the fairness metric can be seen in Figure \ref{['fig-variance']}, similar figures for raw and balanced accuracy can be seen in Figure \ref{['fig-performance-fairness-acc']}. An https://reliable-ai.github.io/fairml-multiverse/ of this figure is available.
• Figure 4: The influence of decisions on the fairness metric can only be understood when examining interactions on top of individual decisions. Visualization of the fairness metric depending on the three most important decision / decision combinations (from A - C by importance) and their respective options.
• Figure 5: The fairness metric of the exact same model can be significantly altered by varying its evaluation strategy alone (A) and especially the interaction of different evaluation decisions leads to changes in the fairness metric (B). Overall distribution (A) and raw values (B) of fairness metric (equalized odds difference) for a single model over different decisions regarding its evaluation. The dashed line in A corresponds to the evaluation strategy used in Study 1fn1eval. Both plots display scores for a model showing median variation, to see the same figure for the model with high variation see Figure \ref{['fig-eval-max']} in the Appendix. An https://reliable-ai.github.io/fairml-multiverse/ of A is available, allowing examination of the distribution for any model in the multiverse analysis.