Recently Argumentation Mechanism Design (ArgMD) was introduced as a paradigm for studying argumentation using game-theoretic techniques. To date, this framework has been used to study under what conditions a direct mechanism based on Dung's grounded semantics is strategy-proof (i.e. truth-enforcing) when knowledge of arguments is private to self-interested agents. In this paper, we study Dung's preferred semantics in order to understand under what conditions it is possible to design strategy-proof mechanisms. This is challenging since, unlike with the grounded semantics, there may be multiple preferred extensions, forcing a mechanism to select one. We show that this gives rise to interesting strategic behaviour, and we show that in general it is not possible to have a strategy-proof mechanism that selects amongst the preferred extensions in a non-biased manner. We also investigaet refinements of preferred semantics which induce unique outcomes, namely the skeptical-preferred and ideal semantics.