In this article, we propose an agent-based model of opinion diffusion and voting where influence among individuals and deliberation in a group are mixed. The model is inspired from social modeling, as it describes an iterative process of collective decision-making that repeats a series of interindividual influences and collective deliberation steps, and studies the evolution of opinions and decisions in a group. It also aims at founding a comprehensive model to describe collective decision-making as a combination of two different paradigms: argumentation theory and ABM-influence models, which are not obvious to combine as a formal link between them is required. In our model, we find that deliberation, through the exchange of arguments, reduces the variance of opinions and the proportion of extremists in a population as long as not too much deliberation takes place in the decision processes. Additionally, if we define the correct collective decisions in the system in terms of the arguments that should be accepted, allowing for more deliberation favors convergence towards the correct decisions.