It is common practice in choice modelling to include the socioeconomic characteristics of other members of a household in the utility expressions associated with the preferences of a particular individual. By including household descriptors, the analyst is assuming that other household members can influence the choices made by the household as if the preference weights (or marginal utilities) are reflective of equal influence of all members of a household. In reality it is likely that there is a power relationship that underlies the contribution of the individual whose preferences are being studied and the contribution of other household members, typically proxied by a number of socioeconomic descriptors. In this paper we condition the individual and the household explanatory variables on an additional parameter that represents the influence or power that each agent has in the revelation of the preferences of a sampled individual. Using a data set of the stated choice of automobile fuel type (petrol, diesel, hybrid), we estimate a nonlinear model to identify the strength of the power relationship, and find that the power contribution of the household members to the individuals choice vary across alternatives. The model with the power relationship is found to be a statistical improvement and delivers substantially different elasticities than the traditional model with household characteristics.