Quantifying consensus in stochastic swarms with disruptive individuals

Achieving consensus in collective systems is essential for coordinated behaviour, yet the presence of strongly opinionated minorities can disrupt the overall dynamics. In this work, we study consensus dynamics in stochastic swarms of finite size, focusing on the impact of disruptive agents on group decision-making. First, we propose how to quantify robustness of consensus, by defining consensus as a parametrised property expressed in bounded linear temporal logic (BLTL). Then, we use statistical model checking to compute and compare the robustness landscape in several scenarios where the group decides between two options of different (asymmetric) quality. Finally, we analyse the effects of swarm size to the consensus landscape over two representative models and two types of disruptive agents. Our results reveal that, surprisingly, when groups are deciding between asymmetric options, disruptive agents can play a constructive role towards the optimal group decisions.