  This paper investigates the use of risk measures and theories of choice for
modeling risk-averse route choice and traffic network equilibrium with random
travel times. We interpret the postulates of these theories in the context of
routing, and we identify additive consistency as a plausible and relevant
condition that allows to reduce risk-averse route choice to a standard shortest
path problem. Within the classical theories of choice under risk, we show that
the only preferences that satisfy this consistency property are the ones
induced by the entropic risk measures.
