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How does a group of agents break indecision when deciding about options withqualities that are hard to distinguish? Biological and artificial multi-agentsystems, from honeybees and bird flocks to bacteria, robots, and humans, oftenneed to overcome indecision when choosing among options in situations in whichthe performance or even the survival of the group are at stake. Breakingindecision is also important because in a fully indecisive state agents are notbiased toward any specific option and therefore the agent group is maximallysensitive and prone to adapt to inputs and changes in its environment. Here, wedevelop a mathematical theory to study how decisions arise from the breaking ofindecision. Our approach is grounded in both equivariant and networkbifurcation theory. We model decision from indecision as synchrony-breaking ininfluence networks in which each node is the value assigned by an agent to anoption. First, we show that three universal decision behaviors, namely,deadlock, consensus, and dissensus, are the generic outcomes ofsynchrony-breaking bifurcations from a fully synchronous state of indecision ininfluence networks. Second, we show that all deadlock and consensus valuepatterns and some dissensus value patterns are predicted by the symmetry of theinfluence networks. Third, we show that there are also many `exotic' dissensusvalue patterns. These patterns are predicted by network architecture, but notby network symmetries, through a new synchrony-breaking branching lemma. Thisis the first example of exotic solutions in an application. Numericalsimulations of a novel influence network model illustrate our theoreticalresults.

Breaking indecision in multi-agent, multi-option dynamics