Consensus time in a voter model with concealed and publicly expressed opinions
Authored by Michael T Gastner, Beata Oborny, Mate Gulyas
Date Published: 2018
DOI: 10.1088/1742-5468/aac14a
Sponsors:
European Union
European Research Council (ERC)
Platforms:
No platforms listed
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
Model code not found
Abstract
The voter model is a simple agent-based model to mimic opinion dynamics
in social networks: a randomly chosen agent adopts the opinion of a
randomly chosen neighbour. This process is repeated until a consensus
emerges. Although the basic voter model is theoretically intriguing, it
misses an important feature of real opinion dynamics: it does not
distinguish between an agent's publicly expressed opinion and her inner
conviction. A person may not feel comfortable declaring her conviction
if her social circle appears to hold an opposing view. Here we introduce
the Concealed Voter Model where we add a second, concealed layer of
opinions to the public layer. If an agent's public and concealed
opinions disagree, she can reconcile them by either publicly disclosing
her previously secret point of view or by accepting her public opinion
as inner conviction. We study a complete graph of agents who can choose
from two opinions. We define a martingale M that determines the
probability of all agents eventually agreeing on a particular opinion.
By analyzing the evolution of M in the limit of a large number of
agents, we derive the leading-order terms for the mean and standard
deviation of the consensus time (i.e. the time needed until all opinions
are identical). We thereby give a precise prediction by how much
concealed opinions slow down a consensus.
Tags
Agent-based models
Dynamics
stochastic processes
Exact results
Socio-economic
networks