Multistable binary decision making on networks

TL;DR

This paper introduces a simple network-based binary decision model inspired by social decision making, predicting phase transitions and avalanche behaviors, with implications for understanding decision dynamics on complex networks.

Contribution

It presents a novel binary decision model on networks that predicts phase transitions and avalanche phenomena, extending understanding of social decision processes.

Findings

Discontinuous phase transitions occur across various network types.

Network structure influences fluctuations in avalanche distributions.

The model exhibits a robust 'glassy' spectrum of equilibria on infinite graphs.

Abstract

We propose a simple model for a binary decision making process on a graph, motivated by modeling social decision making with cooperative individuals. The model is similar to a random field Ising model or fiber bundle model, but with key differences on heterogeneous networks. For many types of disorder and interactions between the nodes, we predict discontinuous phase transitions with mean field theory which are largely independent of network structure. We show how these phase transitions can also be understood by studying microscopic avalanches, and describe how network structure enhances fluctuations in the distribution of avalanches. We suggest theoretically the existence of a "glassy" spectrum of equilibria associated with a typical phase, even on infinite graphs, so long as the first moment of the degree distribution is finite. This behavior implies that the model is robust against noise below a certain scale, and also that phase transitions can switch from discontinuous to continuous on networks with too few edges. Numerical simulations suggest that our theory is accurate.