Multi-agent systems are often presented as a solution for dangerous missions, such as search-and-rescue and disaster relief, which require timely decision-making. However, the corresponding environments rarely allow for long range communication or control, and often come with a lack of crucial information for autonomous decision-making (e.g. topology of the area, or number and priority of targets). In this paper, we present a fast collective decision-making framework for robotic swarms, which requires no external infrastructure or pre-existing knowledge. This method is based on running an abstract decision-making model simultaneously with an ad-hoc navigation strategy. We demonstrate the scalability of our proposed method with respect to the swarm size, and its flexibility regarding the number and quality of alternatives, in simulated experiments.