From causality to liability: integrating Bayesian inference and PageRank logic in legal responsibility assessment

Abstract Legal systems across jurisdictions continue to grapple with the inherent difficulty of attributing responsibility in multi-agent scenarios marked by probabilistic causation, distributed actions, and epistemic uncertainty—particularly within the domain of insurance law. Traditional legal tools such as proximate cause tests, fault trees, and intuitive heuristics often fall short in handling such complexity with analytical precision or procedural fairness. This study introduces CausalRank, a novel, hybrid mathematical model that integrates Bayesian conditional probability inference with a PageRank-based influence propagation algorithm to enable structured, recursive, and normatively calibrated allocation of legal responsibility. The model is structured in five computational stages: (i) construction of an Actor-Action-Event (AAE) causal graph, (ii) population of a Bayesian Conditional Probability Matrix (B) reflecting probabilistic dependencies, (iii) recursive scoring of actors’ causal contributions via an adapted PageRank algorithm (CRS), (iv) normative and evidentiary modulation through the Responsibility Distribution Function (RDF), and (v) final liability allocation with full traceability. Unlike existing models, CausalRank captures not only direct causation but also indirect, systemic influence, and adjusts outputs using legal–theoretic variables such as foreseeability, institutional duty, and evidentiary confidence. Through a legally realistic, multi-agent traffic collision scenario, the study demonstrates how CausalRank produces liability distributions that are computationally rigorous, normatively coherent, and empirically explainable. The model’s transparent, modular design supports its integration into legal decision support systems, insurance adjudication frameworks, and regulatory simulation tools. Key strengths include its ability to manage uncertainty, facilitate counterfactual reasoning, and reflect plural forms of responsibility (individual, institutional, and infrastructural). In sum, CausalRank offers not just a technical innovation but a conceptual framework for rethinking how legal responsibility can be allocated in complex, data-rich, and ethically demanding contexts. It advances the field of computational legal reasoning by aligning formal causal models with normative legal principles, providing a foundation for future interdisciplinary research and real-world application.