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.