Additive Consistency of Risk Measures and Its Application to Risk-Averse Routing in Networks

We investigate the use of risk measures and theories of choice to model risk‐averse routing and traffic equilibrium on networks with random travel times. We interpret the postulates of these theories in the context of routing, identifying additive consistency as a plausible condition that allows to reduce risk‐averse route choice to a standard shortest path problem. Within the classical theories of choice, we show that the only preferences that satisfy this condition are the ones induced by the entropic risk measures.