We combine empirical experimental research on biased argument processing with a computational theory of group deliberation to overcome the micro-macro problem of sociology and to clarify the role of biased processing in debates around energy. We integrate biased processing into the framework of argument communication theory in which agents exchange arguments about a certain topic and adapt opinions accordingly. Our derived mathematical model fits significantly better to the experimentally observed attitude changes than the neutral argument processing assumption made in previous models. Our approach provides new insight into the relationship between biased processing and opinion polarization. Our analysis reveals a sharp qualitative transition from attitude moderation to polarization at the individual level. At the collective level, we find that weak biased processing significantly accelerates group decision processes, whereas strong biased processing leads to a meta-stable conflictual state of bi-polarization that becomes persistent as the bias increases.