Consensus formation on heterogeneous networks

Abstract

Reaching consensus -a macroscopic state where almost all the system constituents display the same microscopic state -is a necessity in multiple complex socio-technical and econo-technical systems: their correct functioning ultimately depends on it. In many distributed systems -of which blockchain-based applications are one example -the process of consensus formation is crucial not only for the emergence of a leading majority but for the very system to function. Inspired on this application, but with a broader applicability, we build a minimalistic network model of consensus formation for quantifying how central nodes -with respect to their average distance to others -can leverage on their position to obtain competitive advantage in the consensus process. We show that in a wide range of network topologies, the probability of forming a majority can significantly increase depending on the centrality of nodes that initiate the spreading. Further, we study the role that network topology plays on the consensus process: we show that central nodes in scale-free networks can win consensus in the network even if they broadcast states significantly later than peripheral ones.