To provide convincing recommendations, which can be fully understood and accepted by a decision-maker, a decision-aider must often engage in an interaction and take the decision maker's responses into account. This feedback can lead to revising the model used to represent the preferences of the decision-maker. Our objective in this paper is to equip an artificial decision-aider with this adaptive behavior. To do that, we build on decision theory to propose a principled way to select decision models. Our approach is axiomatic in that it does not only work for a predefined subset of methods---we instead provide the properties that make models compatible with our proposal. Finally, the interaction model is complex since it can involve the exchange of different types of preferential information, as well as others locutions such as justifications. We manage it through a dialogue game, and prove that it satisfies desired properties, in particular termination, and efficiency.