Argument aggregation is the problem of combining argumentation frameworks. An argument aggregation procedure takes as input an argument framework for each agent in a system, intuitively representing the beliefs of that agent with respect to a disputed domain of discourse; the output is an argumentation framework that represents the social position on the domain of discourse. There are clear analogies between argument aggregation and the well-known preference aggregation problem, which has been extensively studied in the social choice community. The first contribution of this paper is to apply some of the methodology developed in social choice theory to argument aggregation. After recalling the basic framework of Dung's abstract argument systems, and introducing the argument aggregation problem, we motivate and formally define a collection of axioms that specific argument aggregation procedures might or might not satisfy. The second contribution of the paper is to consider the analysis of argument aggregation procedures with respect to these various axioms. We consider a natural representation for argument aggregation procedures, based on Boolean circuits. We then investigate the problem of verifying whether an argument aggregation procedure, presented in this way, does or does not satisfy a number of the axioms we introduced.