Nonlinear dynamics of multi-agent multi-option belief and opinion formation

Abstract

Many self-organized collective behaviors in natural, social, and technological groups require coordinated decision-making on multiple alternatives. For example, groups must reach consensus on a movement direction to navigate through space in unison or allocate members across different tasks to forage and explore their environment. In this dissertation we present a new modeling framework for the study of multi-alternative collective decision-making in social systems in nature and society,and for the design of such decision-making in technological teams. First, we describe a new model of social belief and opinion formation as a dynamic and nonlinear process in a multi-agent system. When the agents are identical, the model has a small number of interpretable parameters that characterize intrinsic properties and biases of the networked agents. Belief formation is synthesized through a communication graph that describes a structured set of cooperative and antagonistic relationships between agents, and a belief system graph that describes the logical alignment between options or topics. We present this model alongside analysis grounded in the theory of nonlinear dynamical systems. We establish that the network generically exhibits a sharp transition from a state of indecision among agents to their commitment to strong beliefs or opinions as the amount of attention to social interactions is increased. We investigate how the model parameters, the communication graph, and the belief system graph inform the allocation of agents across options in this transition and the how relative influence of different agents’ biases informs the network decision. We prove conditions under which the belief formation dynamics yield agreement, disagreement, multi-stability of equilibria, and oscillations. Finally, we illustrate how this modeling framework can be utilized for the design of sensitive and adaptable collective behaviors when model parameters are allowed to be dynamic. First, we introduce tunable dynamic feedback laws for agents’ attention to social interactions which provably trigger cascades of strong opinion formation that spread across the entire network in response to a local input. Next, we prove that individual nodes can adapt their decision state locally without affecting the state of the rest of the network through altering the sign of their social interactions.