Authors: Arpan Mukhopadhyay (INRIA, Paris & Bell Labs, France); Ravi R Mazumdar (University of Waterloo, Canada); Rahul Roy (Indian Statistical Institute, Delhi, India)
Presenter bio: Arpan Mukhopadhyay received his Bachelor of Engineering (B.E.) degree in Electronics and Telecommunication Engineering from the Jadavpur University, Kolkata, India in 2009, his Master of Engineering (M.E.) degree in Telecommunication Engineering from the Indian Institute of Science, Bangalore, India in 2011, and his Ph.D in Electrical and Computer Engineering from the University of Waterloo, Canada in 2016. He is currently a post-doctoral researcher jointly working at INRIA, Paris and Bell Labs, France. His research interests are broadly in the area of queueing theory, design and optimization of complex networks, performance analysis, and probabilistic methods.
Abstract: In this paper, we investigate the impact of random interactions
between agents in a social network on the diffusion of opinions
in the network.
Opinion of each agent is assumed to be
a binary variable taking values in the set {0, 1}.
Each agent is assumed to be able to interact with any other agent
in the network.
This models scenarios where
every agent in the network has to choose from two available options
and the size of the neighborhood of each agent is an increasing
function of the total number agents in the network.
It is assumed that each agent updates its opinion at random instants upon interacting
with other randomly sampled agents.
We consider two simple rules of interaction: (1) the voter rule
in which the updating agent simply copies the opinion
of another randomly sampled agent;
(2) the majority rule, in which
the updating agent samples multiple agents
and adopts the majority opinion among
the sampled agents and the agent itself.
Under each rule, we consider
two different scenarios which have note been
considered in the literature thus far: (1) where the agents
are `biased' towards one of the opinions,
(2) where different agents have different degrees of stubbornness.
We show that the presence of biased agents
reduces the consensus time for the voter rule exponentially
as compared to the case where the agents are unbiased.
For the majority rule model with biased agents
we show that the network reaches consensus on a particular opinion
with high probability only when the initial fraction of agents
having that opinion is above a certain threshold.
For the majority rule model with stubborn agents
we observe metastability where the network
switches back and forth between stable states spending long
intervals in each state.
