The Dynamics of Multi-agent Multi-option Decision Making

Decision making is a dynamical phenomenon and thus the transition from indecision to decision can be described well by bifurcation theory. Agreement, or consensus, is only one of many ways in which collective decisions can be made. However, theories of multi-agent multi-option decision making either focus on agreement decisions or average at the agent level to achieve a mean-field description of the decision dynamics. Introducing the agent level back into collective decision-making models uncovers a plethora of novel collective behaviors beyond agreement and mean-field descriptions of disagreement and polarization. These include uniform and moderate-extremist disagreement, and switchy-and-fast versus continuous-and-slow transitions from indecision to decision. Which of these behaviors emerge depends on the model parameters, in particular, the number of agents and the number of options. Our study is grounded in Equivariant Bifurcation Theory, which allows us to formulate model-independent predictions and to develop a constructive sensitivity analysis of the decision dynamics at the organizing equivariant singularity. The localized sensitivity analysis reveals how collective decision making can be both flexible and robust in response to subtle changes in the environment or in the deciding agent interactions. Equivariant Bifurcation Theory also guides the construction of new multi-agent multi-option decision-making dynamics, for an arbitrary number of agents and an arbitrary number of options, and with fully controllable dynamical behaviors.