Competing local and global interactions in social dynamics: how important is the friendship network?

TL;DR

This paper investigates how different combinations of local and global social interactions influence consensus formation in social networks, revealing the significant impact of network structure and interaction ranges.

Contribution

It introduces a comprehensive analysis of the $q$-voter model with mixed local and global conformity and anticonformity, highlighting the role of network topology.

Findings

Local conformity with global anticonformity makes consensus difficult.

Network structure significantly affects the model with local conformity.

Swapping interaction ranges reduces sensitivity to network topology.

Abstract

Motivated by the empirical study that identifies a correlation between particular social responses and different interaction ranges, we study the $q$-voter model with various combinations of local and global sources of conformity and anticonformity. The models are investigated by means of the pair approximation and Monte Carlo simulations on Watts-Strogatz and Barab\'{a}si-Albert networks. We show that within the model with local conformity and global anticonformity, the agreement in the system is the most difficult to achieve, and the role of the network structure is the most significant. Interestingly, the model with swapped interaction ranges, namely with global conformity and local anticonformity, becomes almost insensitive to the changes in the network structure. The obtained results may have far reaching consequences for marketing strategies conducted via social media channels.