13 research outputs found
Opinion Formation in Laggard Societies
We introduce a statistical physics model for opinion dynamics on random
networks where agents adopt the opinion held by the majority of their direct
neighbors only if the fraction of these neighbors exceeds a certain threshold,
p_u. We find a transition from total final consensus to a mixed phase where
opinions coexist amongst the agents. The relevant parameters are the relative
sizes in the initial opinion distribution within the population and the
connectivity of the underlying network. As the order parameter we define the
asymptotic state of opinions. In the phase diagram we find regions of total
consensus and a mixed phase. As the 'laggard parameter' p_u increases the
regions of consensus shrink. In addition we introduce rewiring of the
underlying network during the opinion formation process and discuss the
resulting consequences in the phase diagram.Comment: 5 pages, eps fig
Outflow Dynamics in Modeling Oligopoly Markets: The Case of the Mobile Telecommunications Market in Poland
In this paper we introduce two models of opinion dynamics in oligopoly
markets and apply them to a situation, where a new entrant challenges two
incumbents of the same size. The models differ in the way the two forces
influencing consumer choice -- (local) social interactions and (global)
advertising -- interact. We study the general behavior of the models using the
Mean Field Approach and Monte Carlo simulations and calibrate the models to
data from the Polish telecommunications market. For one of the models
criticality is observed -- below a certain critical level of advertising the
market approaches a lock-in situation, where one market leader dominates the
market and all other brands disappear. Interestingly, for both models the best
fits to real data are obtained for conformity level . This
agrees very well with the conformity level found by Solomon Asch in his famous
social experiment
Ising model with memory: coarsening and persistence properties
We consider the coarsening properties of a kinetic Ising model with a memory
field. The probability of a spin-flip depends on the persistence time of the
spin in a state. The more a spin has been in a given state, the less the
spin-flip probability is. We numerically studied the growth and persistence
properties of such a system on a two dimensional square lattice. The memory
introduces energy barriers which freeze the system at zero temperature. At
finite temperature we can observe an apparent arrest of coarsening for low
temperature and long memory length. However, since the energy barriers
introduced by memory are due to local effects, there exists a timescale on
which coarsening takes place as for the Ising model. Moreover the two point
correlation functions of the Ising model with and without memory are the same,
indicating that they belong to the same universality class.Comment: 10 pages, 7 figures; some figures and some comments adde
Analytical Solution of the Voter Model on Disordered Networks
We present a mathematical description of the voter model dynamics on
heterogeneous networks. When the average degree of the graph is
the system reaches complete order exponentially fast. For , a finite
system falls, before it fully orders, in a quasistationary state in which the
average density of active links (links between opposite-state nodes) in
surviving runs is constant and equal to , while an
infinite large system stays ad infinitum in a partially ordered stationary
active state. The mean life time of the quasistationary state is proportional
to the mean time to reach the fully ordered state , which scales as , where is the number of nodes of the
network, and is the second moment of the degree distribution. We find
good agreement between these analytical results and numerical simulations on
random networks with various degree distributions.Comment: 20 pages, 8 figure
Some new results on one-dimensional outflow dynamics
In this paper we introduce modified version of one-dimensional outflow
dynamics (known as a Sznajd model) which simplifies the analytical treatment.
We show that simulations results of the original and modified rules are exactly
the same for various initial conditions. We obtain the analytical formula for
exit probability using Kirkwood approximation and we show that it agrees
perfectly with computer simulations in case of random initial conditions.
Moreover, we compare our results with earlier analytical calculations obtained
from renormalization group and from general sequential probabilistic frame
introduced by Galam. Using computer simulations we investigate the time
evolution of several correlation functions to show if Kirkwood approximation
can be justified. Surprisingly, it occurs that Kirkwood approximation gives
correct results even for these initial conditions for which it cannot be easily
justified.Comment: 6 pages, 7 figure
Opinion Dynamics of Learning Agents: Does Seeking Consensus Lead to Disagreement?
We study opinion dynamics in a population of interacting adaptive agents
voting on a set of complex multidimensional issues. We consider agents which
can classify issues into for or against. The agents arrive at the opinions
about each issue in question using an adaptive algorithm. Adaptation comes from
learning and the information for the learning process comes from interacting
with other neighboring agents and trying to change the internal state in order
to concur with their opinions. The change in the internal state is driven by
the information contained in the issue and in the opinion of the other agent.
We present results in a simple yet rich context where each agent uses a Boolean
Perceptron to state its opinion. If there is no internal clock, so the update
occurs with asynchronously exchanged information among pairs of agents, then
the typical case, if the number of issues is kept small, is the evolution into
a society thorn by the emergence of factions with extreme opposite beliefs.
This occurs even when seeking consensus with agents with opposite opinions. The
curious result is that it is learning from those that hold the same opinions
that drives the emergence of factions. This results follows from the fact that
factions are prevented by not learning at all from those agents that hold the
same opinion. If the number of issues is large, the dynamics becomes trapped
and the society does not evolve into factions and a distribution of moderate
opinions is observed. We also study the less realistic, but technically simpler
synchronous case showing that global consensus is a fixed point. However, the
approach to this consensus is glassy in the limit of large societies if agents
adapt even in the case of agreement.Comment: 16 pages, 10 figures, revised versio
Algebraic coarsening in voter models with intermediate states
The introduction of intermediate states in the dynamics of the voter model
modifies the ordering process and restores an effective surface tension. The
logarithmic coarsening of the conventional voter model in two dimensions is
eliminated in favour of an algebraic decay of the density of interfaces with
time, compatible with Model A dynamics at low temperatures. This phenomenon is
addressed by deriving Langevin equations for the dynamics of appropriately
defined continuous fields. These equations are analyzed using field theoretical
arguments and by means of a recently proposed numerical technique for the
integration of stochastic equations with multiplicative noise. We find good
agreement with lattice simulations of the microscopic model.Comment: 11 pages, 5 figures; minor typos correcte
Mass Media Influence Spreading in Social Networks with Community Structure
We study an extension of Axelrod's model for social influence, in which
cultural drift is represented as random perturbations, while mass media are
introduced by means of an external field. In this scenario, we investigate how
the modular structure of social networks affects the propagation of mass media
messages across the society. The community structure of social networks is
represented by coupled random networks, in which two random graphs are
connected by intercommunity links. Considering inhomogeneous mass media fields,
we study the conditions for successful message spreading and find a novel phase
diagram in the multidimensional parameter space. These findings show that
social modularity effects are of paramount importance in order to design
successful, cost-effective advertising campaigns.Comment: 21 pages, 9 figures. To appear in JSTA
Generic modes of consensus formation in stochastic language dynamics
We introduce a class of stochastic models for the dynamics of two linguistic
variants that are competing to become the single, shared convention within an
unstructured community of speakers. Different instances of the model are
distinguished by the way agents handle variability in the language (i.e.,
multiple forms for the same meaning). The class of models includes as special
cases two previously-studied models of language dynamics, the Naming Game, in
which agents tend to standardise on variants they have encountered most
frequently, and the Utterance Selection Model, in which agents tend to preserve
variability by uniform sampling of a pool of utterances. We reduce the full
complexities of the dynamics to a single-coordinate stochastic model which
allows the probability and time taken for speakers to reach consensus on a
single variant to be calculated for large communities. This analysis suggests
that in the broad class of models considered, consensus is formed in one of
three generic ways, according to whether agents tend to eliminate, accentuate
or sample neutrally the variability in the language. These different regimes
are observed in simulations of the full dynamics, and for which the simplified
model in some cases makes good quantitative predictions. We use these results,
along with comparisons with related models, to conjecture the likely behaviour
of more general models, and further make use of empirical data to argue that in
reality, biases away from neutral sampling behaviour are likely to be small.Comment: 36 pages; 22 eps figures; embarrassing sign error in v2 corrected; to
appear J Stat Mec