9,921 research outputs found
Binary and Multivariate Stochastic Models of Consensus Formation
A current paradigm in computer simulation studies of social sciences problems
by physicists is the emergence of consensus. The question is to establish when
the dynamics of a set of interacting agents that can choose among several
options (political vote, opinion, cultural features, etc.) leads to a consensus
in one of these options, or when a state with several coexisting social options
prevail. We consider here stochastic dynamic models naturally studied by
computer simulations. We will first review some basic results for the voter
model. This is a binary option stochastic model, and probably the simplest
model of collective behavior. Next we consider a model proposed by Axelrod for
the dissemination of culture. This model can be considered as a multivariable
elaboration of the voter model dynamics.Comment: (16 pages, 8 figures; for simililar work visit
http://www.imedea.uib.es/physdept
Deriving mesoscopic models of collective behaviour for finite populations
Animal groups exhibit emergent properties that are a consequence of local
interactions. Linking individual-level behaviour to coarse-grained descriptions
of animal groups has been a question of fundamental interest. Here, we present
two complementary approaches to deriving coarse-grained descriptions of
collective behaviour at so-called mesoscopic scales, which account for the
stochasticity arising from the finite sizes of animal groups. We construct
stochastic differential equations (SDEs) for a coarse-grained variable that
describes the order/consensus within a group. The first method of construction
is based on van Kampen's system-size expansion of transition rates. The second
method employs Gillespie's chemical Langevin equations. We apply these two
methods to two microscopic models from the literature, in which organisms
stochastically interact and choose between two directions/choices of foraging.
These `binary-choice' models differ only in the types of interactions between
individuals, with one assuming simple pair-wise interactions, and the other
incorporating higher-order effects. In both cases, the derived mesoscopic SDEs
have multiplicative, or state-dependent, noise. However, the different models
demonstrate the contrasting effects of noise: increasing order in the pair-wise
interaction model, whilst reducing order in the higher-order interaction model.
Although both methods yield identical SDEs for such binary-choice, or
one-dimensional, systems, the relative tractability of the chemical Langevin
approach is beneficial in generalizations to higher-dimensions. In summary,
this book chapter provides a pedagogical review of two complementary methods to
construct mesoscopic descriptions from microscopic rules and demonstrates how
resultant multiplicative noise can have counter-intuitive effects on shaping
collective behaviour.Comment: Second version, 4 figures, 2 appendice
Learning and Forecasting Opinion Dynamics in Social Networks
Social media and social networking sites have become a global pinboard for
exposition and discussion of news, topics, and ideas, where social media users
often update their opinions about a particular topic by learning from the
opinions shared by their friends. In this context, can we learn a data-driven
model of opinion dynamics that is able to accurately forecast opinions from
users? In this paper, we introduce SLANT, a probabilistic modeling framework of
opinion dynamics, which represents users opinions over time by means of marked
jump diffusion stochastic differential equations, and allows for efficient
model simulation and parameter estimation from historical fine grained event
data. We then leverage our framework to derive a set of efficient predictive
formulas for opinion forecasting and identify conditions under which opinions
converge to a steady state. Experiments on data gathered from Twitter show that
our model provides a good fit to the data and our formulas achieve more
accurate forecasting than alternatives
Modeling of the parties' vote share distributions
Competition between varying ideas, people and institutions fuels the dynamics
of socio-economic systems. Numerous analyses of the empirical data extracted
from different financial markets have established a consistent set of stylized
facts describing statistical signatures of the competition in the financial
markets. Having an established and consistent set of stylized facts helps to
set clear goals for theoretical models to achieve. Despite similar abundance of
empirical analyses in sociophysics, there is no consistent set of stylized
facts describing the opinion dynamics. In this contribution we consider the
parties' vote share distributions observed during the Lithuanian parliamentary
elections. We show that most of the time empirical vote share distributions
could be well fitted by numerous different distributions. While discussing this
peculiarity we provide arguments, including a simple agent-based model, on why
the beta distribution could be the best choice to fit the parties' vote share
distributions.Comment: 12 pages, 7 figure
Large population and long-term behavior of a stochastic binary opinion model
We propose and study a stochastic binary opinion model where agents in a
group are considered to hold an opinion of 0 or 1 at each moment. An agent in
the group updates his/her opinion based on the group's opinion configuration
and his/her \emph{personality}. Considering the number of agents with opinion 1
as a continuous time Markov process, we analyze the long-term probabilities for
large population size in relation to the personalities of the group. In
particular, we focus on the question of "balance" where both opinions are
present in nearly equal numbers as opposed to "dominance" where one opinion is
dominant
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