Optimal Explanations: A Quantitative Model of Human Error in Causal Graph Interpretation

When Artificial Intelligence (AI) reasoning is explained via causal graphs for human oversight, the human-computer interface is the performance bottleneck for decision-supported actions. As explanations grow more complex, humans' interpretation ability degrades, resulting in ineffective oversight. This paper contributes a quantitative model of human causal reasoning bounds and demonstrates their utility for interpretable AI explanations. Our empirical contribution is a large-scale user study (n=170), allowing the quantification of the bounded human rationality for understanding causal explanations by measuring the impact of the causal complexity on human understanding. Our significant results reveal that users are bounded causal reasoners: while their decision time increases linearly with each added factor (0.65 seconds per node), our data suggests their decision errors increase exponentially. This indicates a cognitive bound on the complexity a user can effectively manage and grounds our framework for establishing a cognitively optimized complexity. Utilizing this evidence, we contribute a theoretical framework, formalizing the influence of explanation complexity on human interpretation error. Based on our empirical results, we introduce a novel method to systematically prune causal explanations to the point of optimal complexity, trading off the explanation's fidelity loss with interpretation error, resulting in an explanation with optimized complexity for human cognitive bounds for directed acyclic graphs with up to 4 relevant nodes and novice users. Our work thereby quantifies the fidelity-interpretability trade-off as a direct relationship between model complexity and interpretation error, providing the foundation for designing structure-aware, explainable AI interfaces, minimizing error for optimal human-AI collaboration.