# Quantifying the impact of network structure on speed and accuracy in collective decision-making

## TL;DR

This paper investigates how network structure influences the speed and accuracy of binary decision-making in collective systems, revealing key spectral properties that predict performance and exploring effects of hierarchical topology.

## Contribution

It introduces spectral measures like eigenvalues and participation ratios as predictors of decision accuracy and analyzes hierarchical network effects on collective computation.

## Key findings

- Decision accuracy is mainly influenced by spectral properties of the network.
- Eigenvalues and participation ratios predict performance scaling in large networks.
- Hierarchical structures like rich clubs affect localization and decision dynamics.

## Abstract

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.