  Found in varied contexts from neurons to ants to fish, binary decision-making
is one of the simplest forms of collective computation. In this process,
information collected by individuals about an uncertain environment is
accumulated to guide behavior at the aggregate scale. We study binary
decision-making dynamics in networks responding to inputs with small
signal-to-noise ratios, looking for quantitative measures of collectivity that
control decision-making performance. We find that decision accuracy is
controlled largely by three factors: the leading eigenvalue of the network
adjacency matrix, the corresponding eigenvector's participation ratio, and
distance from the corresponding symmetry-breaking bifurcation. This allows us
to predict how decision-making performance scales in large networks based on
their spectral properties. Specifically, we explore the effects of localization
caused by the hierarchical assortative structure of a "rich club" topology.
This gives insight into the tradeoffs involved in the higher-order structure
found in living networks performing collective computations.
