Social influences play an important part in the actions that an individual agent may perform within a multi-agent society. However, the incomplete knowledge and the diverse and conflicting influences present within such societies, may stop an agent from abiding by all its social influences. This may, in turn, lead to conflicts that the agents need to identify, manage, and resolve in order for the society to behave in a coherent manner. To this end, we present an empirical study of an argumentation-based negotiation (ABN) approach that allows the agents to detect such conflicts, and then manage and resolve them through the use of argumentative dialogues. To test our theory, we map our ABN model to a multi-agent task allocation scenario. Our results show that using an argumentation approach allows agents to both efficiently and effectively manage their social influences even under high degrees of incompleteness. Finally, we show that allowing agents to argue and resolve such conflicts early in the negotiation encounter increases their efficiency in managing social influences.