Recent work in travel demand modeling has sought to address decision making under risk and uncertainty by bringing together elements of expected utility theory (EUT) and random utility theory (RUT). The aims are to identify and discuss the key theoretical issues associated with the merging of EUT and RUT in a transport context and then to explore the many empirical issues associated with the specification of attitudes to risk. Specifically, the performance of the alternative specification of attitudes to risk is investigated with the use of data from a large stated-preference exercise in which respondents were faced with a series of choices between alternative unreliable train services.