  Public opinion is subject to peer interaction via social networks and
external pressure from the media, advertising, and other actors. In this paper,
we study the interaction between external and peer influence on the stochastic
opinion dynamics of a majority vote model. We introduce a model where agents
update their opinions based on the combined influence of their local
neighbourhood (peers) and an external actor in the transition rates. In the
first model, the external influence is only felt by agents non-aligned with the
external actor ("push strategy"). In the second model, agents are affected by
external influence, independently of their opinions ("nudging strategy"). In
both cases, the external influence increases the possible macroscopic outcomes.
These outcomes are determined by the chosen influence strategy. We also find
that the social network structure affects the opinion dynamics, with social
clustering positively reinforcing the external influence whereas degree
heterogeneity weakens the external forces. These findings are relevant to
businesses and policy making, helping to understand how groups of individuals
collectively react to external actors.
