From Risk Theory to Road Safety: Developing an Axiomatic Risk Measure for Connected and Automated Vehicles (CAVs)

Existing risk assessment methods like rule, risk, judgement, event, and vulnerability-impact based offer valuable insights for assessment of CAV safety. However, risk and safety remain contested concepts: risk is measured quantitatively, while safety provides normative reference boundaries defined outside the risk model. This paper reviews different approaches to risk assessment, their methods and their numerical measures, including probabilistic distributions, quantile thresholds, impact-based scoring, and composite indices. Sectoral exemplars from aviation, finance, medicine, rail, and cybersecurity show how each discipline operationalizes risk and the principles or axioms governing those practices. Together, these perspectives reveal both the diversity of risk methods and their shared limitations when applied in dynamic traffic scenarios. Drawing on the strengths and limitations identified across the sectoral exemplars, the paper proposes an axiomatic, real-time, risk measure for CAVs based on the probability-of-exceedance. Denoted P_γ, the measure quantifies the proportion of safety scores (e.g., time-to-collision) that fall below a critical threshold γ, under a probabilistic model, i.e., behaviour of other actors, weather and road conditions. The measure links probabilistic risk estimation to normative safety boundaries (e.g., thresholds derived from road rules), supports composite safety scoring, and enables time-consistent updating as new information becomes available. The result, a conceptual framework founded on the axioms of monotonicity, subadditivity, translation invariance, positive homogeneity, time-consistency, and interpretability, and is demonstrated through a worked scenario. The framework provides a foundation for empirical estimation of the proposed risk measure using Monte Carlo simulation under dependent, multi-actor environment models, with future work using expert elicitation to support the axiomatic grounding of the framework.