Argumentation has been acknowledged as a powerful mechanism for automated decision making. In this context several recent works have studied the problem of accommodating preference information in argumentation. The majority of these studies rely on Dung’s abstract argumentation framework and its underlying acceptability semantics. In this paper we show that Dung’s acceptability semantics, when applied to a preference-based argumentation framework for decision making purposes, may lead to counter intuitive results, as it does not take appropriately into account the preference information. To remedy this we propose a new acceptability semantics, called super-stable extension semantics, and present some of its properties. Moreover, we show that argumentation can be understood as a multiple criteria decision problem, making in this way results from decision theory applicable to argumentation.