This paper is concerned with the general problem of constructing decision tables and more specifically, with the identification of all possible outcomes of decisions. We introduce and propose basic influence diagrams as a simple way of describing problems of decision making under strict uncertainty. We then establish a correspondence between basic influence diagrams and symmetric generalised assumption-based argumentation frameworks and adopt an argumentation-based approach to identify the possible outcomes. We show that the intended solutions are best characterised using a new semantics that we call liberal stability. We finally present a number of theoretical results concerning the relationships between liberal stability and existing semantics for argumentation.