Collective Robustness of Heterogeneous Decision-Makers Against Stubborn Individuals

Abstract

Can heterogeneity be a cost-effective solution for swarm robotics? Motivated by what we see in animal groups, especially eusocial insect colonies, that exploit behavioural heterogeneity as the cornerstone of their success, we investigate whether or not swarms of robots with different behaviours can be more cost-effective than homogeneous swarms. We focus on the process of collective decision-making where robots must achieve a consensus on the best alternative between two options with different qualities, the best-of-2 problem. We consider four behaviours from the literature where robots use rules of voter-like models to exchange and update their opinions. We study the swarm's ability to be robust to the presence of zealots, i.e., stubborn robots that do not change their opinions. Our analysis is based on mean-field models that describe the change of the sub-populations holding different opinions. We show that heterogeneous swarms can be more efficient when we include in the analysis the cost of social interactions between robots. Normally, more interactive behaviours (e.g., pooling many neighbours' opinions at each timestep rather than one per timestep) are quicker in making a decision and more robust to zealots. Heterogeneous swarms combine high performance with lower costs, as not the entire group must be highly interactive to maximise collective performance. Our results are useful when seeking a balance between making accurate collective decisions and minimising the cost of social interactions, the objective of artificial and natural swarms.