Consensus formation on heterogeneous networks

Abstract

Reaching consensus—a macroscopic state where the system constituents display the same microscopic state—is a necessity in multiple complex socio-technical and techno-economic systems: their correct functioning ultimately depends on it. In many distributed systems—of which blockchain-based applications are a paradigmatic example—the process of consensus formation is crucial not only for the emergence of a leading majority but for the very functioning of the system. We build a minimalistic network model of consensus formation on blockchain systems 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.