30,274 research outputs found
Comment on "Mixing beliefs among interacting agents"
We comment on the derivation of the main equation in the bounded confidence
model of opinion dynamics. In the original work, the equation is derived using
an ad-hoc counting method. We point that the original derivation does contain
some small mistake. The mistake does not have a large qualitative impact, but
it reveals the danger of the ad-hoc counting method. We show how a more
systematic approach, which we call micro to macro, can avoid such mistakes,
without adding any significant complexity.Comment: 7 page
Opinion fluctuations and disagreement in social networks
We study a tractable opinion dynamics model that generates long-run
disagreements and persistent opinion fluctuations. Our model involves an
inhomogeneous stochastic gossip process of continuous opinion dynamics in a
society consisting of two types of agents: regular agents, who update their
beliefs according to information that they receive from their social neighbors;
and stubborn agents, who never update their opinions. When the society contains
stubborn agents with different opinions, the belief dynamics never lead to a
consensus (among the regular agents). Instead, beliefs in the society fail to
converge almost surely, the belief profile keeps on fluctuating in an ergodic
fashion, and it converges in law to a non-degenerate random vector. The
structure of the network and the location of the stubborn agents within it
shape the opinion dynamics. The expected belief vector evolves according to an
ordinary differential equation coinciding with the Kolmogorov backward equation
of a continuous-time Markov chain with absorbing states corresponding to the
stubborn agents and converges to a harmonic vector, with every regular agent's
value being the weighted average of its neighbors' values, and boundary
conditions corresponding to the stubborn agents'. Expected cross-products of
the agents' beliefs allow for a similar characterization in terms of coupled
Markov chains on the network. We prove that, in large-scale societies which are
highly fluid, meaning that the product of the mixing time of the Markov chain
on the graph describing the social network and the relative size of the
linkages to stubborn agents vanishes as the population size grows large, a
condition of \emph{homogeneous influence} emerges, whereby the stationary
beliefs' marginal distributions of most of the regular agents have
approximately equal first and second moments.Comment: 33 pages, accepted for publication in Mathematics of Operation
Researc
Dynamical affinity in opinion dynamics modelling
We here propose a model to simulate the process of opinion formation, which
accounts for the mutual affinity between interacting agents. Opinion and
affinity evolve self-consistently, manifesting a highly non trivial interplay.
A continuous transition is found between single and multiple opinion states.
Fractal dimension and signature of critical behaviour are also reported. A rich
phenomenology is presented and discussed with reference to corresponding
psychological implications
Collective dynamics of belief evolution under cognitive coherence and social conformity
Human history has been marked by social instability and conflict, often
driven by the irreconcilability of opposing sets of beliefs, ideologies, and
religious dogmas. The dynamics of belief systems has been studied mainly from
two distinct perspectives, namely how cognitive biases lead to individual
belief rigidity and how social influence leads to social conformity. Here we
propose a unifying framework that connects cognitive and social forces together
in order to study the dynamics of societal belief evolution. Each individual is
endowed with a network of interacting beliefs that evolves through interaction
with other individuals in a social network. The adoption of beliefs is affected
by both internal coherence and social conformity. Our framework explains how
social instabilities can arise in otherwise homogeneous populations, how small
numbers of zealots with highly coherent beliefs can overturn societal
consensus, and how belief rigidity protects fringe groups and cults against
invasion from mainstream beliefs, allowing them to persist and even thrive in
larger societies. Our results suggest that strong consensus may be insufficient
to guarantee social stability, that the cognitive coherence of belief-systems
is vital in determining their ability to spread, and that coherent
belief-systems may pose a serious problem for resolving social polarization,
due to their ability to prevent consensus even under high levels of social
exposure. We therefore argue that the inclusion of cognitive factors into a
social model is crucial in providing a more complete picture of collective
human dynamics
Consensus Emerging from the Bottom-up: the Role of Cognitive Variables in Opinion Dynamics
The study of opinions e.g., their formation and change, and their effects
on our society by means of theoretical and numerical models has been one of
the main goals of sociophysics until now, but it is one of the defining topics
addressed by social psychology and complexity science. Despite the flourishing
of different models and theories, several key questions still remain
unanswered. The aim of this paper is to provide a cognitively grounded
computational model of opinions in which they are described as mental
representations and defined in terms of distinctive mental features. We also
define how these representations change dynamically through different
processes, describing the interplay between mental and social dynamics of
opinions. We present two versions of the model, one with discrete opinions
(voter model-like), and one with continuous ones (Deffuant-like). By means of
numerical simulations, we compare the behaviour of our cognitive model with the
classical sociophysical models, and we identify interesting differences in the
dynamics of consensus for each of the models considered.Comment: 14 pages, 8 figure
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