237 research outputs found
Opinion dynamics in a three-choice system
We generalize Galam's model of opinion spreading by introducing three
competing choices. At each update, the population is randomly divided in groups
of three agents, whose members adopt the opinion of the local majority. In the
case of a tie, the local group adopts opinion A, B or C with probabilities
alpha, beta and (1-alpha-beta) respectively. We derive the associated phase
diagrams and dynamics by both analytical means and simulations. Polarization is
always reached within very short time scales. We point out situations in which
an initially very small minority opinion can invade the whole system.Comment: To appear in European Physical Journal B. A few errors corrected,
some figures redrawn from the first versio
Self-consistency and Symmetry in d-dimensions
Bethe approximation is shown to violate Bravais lattices translational
invariance. A new scheme is then presented which goes over the one-site Weiss
model yet preserving initial lattice symmetry. A mapping to a one-dimensional
finite closed chain in an external field is obtained. Lattice topology
determines the chain size. Using recent results in percolation, lattice
connectivity between chains is argued to be where is the
coordination number and is the space dimension. A new self-consistent
mean-field equation of state is derived. Critical temperatures are thus
calculated for a large variety of lattices and dimensions. Results are within a
few percent of exact estimates. Moreover onset of phase transitions is found to
occur in the range . For the Ising hypercube it yields the Golden
number limit .Comment: 16 pages, latex, Phys. Rev. B (in press
Consensus Formation in Multi-state Majority and Plurality Models
We study consensus formation in interacting systems that evolve by
multi-state majority rule and by plurality rule. In an update event, a group of
G agents (with G odd), each endowed with an s-state spin variable, is
specified. For majority rule, all group members adopt the local majority state;
for plurality rule the group adopts the local plurality state. This update is
repeated until a final consensus state is generally reached. In the mean field
limit, the consensus time for an N-spin system increases as ln N for both
majority and plurality rule, with an amplitude that depends on s and G. For
finite spatial dimensions, domains undergo diffusive coarsening in majority
rule when s or G is small. For larger s and G, opinions spread ballistically
from the few groups with an initial local majority. For plurality rule, there
is always diffusive domain coarsening toward consensus.Comment: 8 pages, 11 figures, 2-column revtex4 format. Updated version: small
changes in response to referee comments. For publication in J Phys
Square lattice site percolation at increasing ranges of neighbor interactions
We report site percolation thresholds for square lattice with neighbor
interactions at various increasing ranges. Using Monte Carlo techniques we
found that nearest neighbors (N), next nearest neighbors (N), next next
nearest neighbors (N) and fifth nearest neighbors (N) yield the same
. At odds, fourth nearest neighbors (N) give .
These results are given an explanation in terms of symmetry arguments. We then
consider combinations of various ranges of interactions with (N+N),
(N+N), (N+N+N) and (N+N). The calculated associated
thresholds are respectively . The
existing Galam--Mauger universal formula for percolation thresholds does not
reproduce the data showing dimension and coordination number are not sufficient
to build a universal law which extends to complex lattices.Comment: 4 pages, revtex
Global culture: A noise induced transition in finite systems
We analyze the effect of cultural drift, modeled as noise, in Axelrod's model
for the dissemination of culture. The disordered multicultural configurations
are found to be metastable. This general result is proven rigorously in d=1,
where the dynamics is described in terms of a Lyapunov potential. In d=2, the
dynamics is governed by the average relaxation time T of perturbations. Noise
at a rate r 1/T sustains
disorder. In the thermodynamic limit, the relaxation time diverges and global
polarization persists in spite of a dynamics of local convergence.Comment: 4 pages, 5 figures. For related material visit
http://www.imedea.uib.es/physdept
Majority Rule Dynamics in Finite Dimensions
We investigate the long-time behavior of a majority rule opinion dynamics
model in finite spatial dimensions. Each site of the system is endowed with a
two-state spin variable that evolves by majority rule. In a single update
event, a group of spins with a fixed (odd) size is specified and all members of
the group adopt the local majority state. Repeated application of this update
step leads to a coarsening mosaic of spin domains and ultimate consensus in a
finite system. The approach to consensus is governed by two disparate time
scales, with the longer time scale arising from realizations in which spins
organize into coherent single-opinion bands. The consequences of this
geometrical organization on the long-time kinetics are explored.Comment: 8 pages, 2-column revtex format, 11 figures. Version 2: minor changes
in response to referee comments and typos corrected; final version for PR
Majority versus minority dynamics: Phase transition in an interacting two-state spin system
We introduce a simple model of opinion dynamics in which binary-state agents
evolve due to the influence of agents in a local neighborhood. In a single
update step, a fixed-size group is defined and all agents in the group adopt
the state of the local majority with probability p or that of the local
minority with probability 1-p. For group size G=3, there is a phase transition
at p_c=2/3 in all spatial dimensions. For p>p_c, the global majority quickly
predominates, while for p<p_c, the system is driven to a mixed state in which
the densities of agents in each state are equal. For p=p_c, the average
magnetization (the difference in the density of agents in the two states) is
conserved and the system obeys classical voter model dynamics. In one dimension
and within a Kirkwood decoupling scheme, the final magnetization in a
finite-length system has a non-trivial dependence on the initial magnetization
for all p.ne.p_c, in agreement with numerical results. At p_c, the exact 2-spin
correlation functions decay algebraically toward the value 1 and the system
coarsens as in the classical voter model.Comment: 11 pages, 3 figures, revtex4 2-column format; minor revisions for
publication in PR
PageRank model of opinion formation on social networks
We propose the PageRank model of opinion formation and investigate its rich
properties on real directed networks of Universities of Cambridge and Oxford,
LiveJournal and Twitter. In this model the opinion formation of linked electors
is weighted with their PageRank probability. We find that the society elite,
corresponding to the top PageRank nodes, can impose its opinion to a
significant fraction of the society. However, for a homogeneous distribution of
two opinions there exists a bistability range of opinions which depends on a
conformist parameter characterizing the opinion formation. We find that
LiveJournal and Twitter networks have a stronger tendency to a totalitar
opinion formation. We also analyze the Sznajd model generalized for scale-free
networks with the weighted PageRank vote of electors.Comment: revtex 10 pages, 16 figs, research at
http://www.quantware.ups-tlse.fr
Dynamics of Majority Rule
We introduce a 2-state opinion dynamics model where agents evolve by majority
rule. In each update, a group of agents is specified whose members then all
adopt the local majority state. In the mean-field limit, where a group consists
of randomly-selected agents, consensus is reached in a time that scales ln N,
where N is the number of agents. On finite-dimensional lattices, where a group
is a contiguous cluster, the consensus time fluctuates strongly between
realizations and grows as a dimension-dependent power of N. The upper critical
dimension appears to be larger than 4. The final opinion always equals that of
the initial majority except in one dimension.Comment: 4 pages, 3 figures, 2-column revtex4 format; annoying typo fixed in
Eq.(1); a similar typo fixed in Eq.(6) and some references update
Noisy continuous--opinion dynamics
We study the Deffuant et al. model for continuous--opinion dynamics under the
influence of noise. In the original version of this model, individuals meet in
random pairwise encounters after which they compromise or not depending of a
confidence parameter. Free will is introduced in the form of noisy
perturbations: individuals are given the opportunity to change their opinion,
with a given probability, to a randomly selected opinion inside the whole
opinion space. We derive the master equation of this process. One of the main
effects of noise is to induce an order-disorder transition. In the disordered
state the opinion distribution tends to be uniform, while for the ordered state
a set of well defined opinion groups are formed, although with some opinion
spread inside them. Using a linear stability analysis we can derive approximate
conditions for the transition between opinion groups and the disordered state.
The master equation analysis is compared with direct Monte-Carlo simulations.
We find that the master equation and the Monte-Carlo simulations do not always
agree due to finite-size induced fluctuations that we analyze in some detail
- …