9,001 research outputs found
Evolution of opinions on social networks in the presence of competing committed groups
Public opinion is often affected by the presence of committed groups of
individuals dedicated to competing points of view. Using a model of pairwise
social influence, we study how the presence of such groups within social
networks affects the outcome and the speed of evolution of the overall opinion
on the network. Earlier work indicated that a single committed group within a
dense social network can cause the entire network to quickly adopt the group's
opinion (in times scaling logarithmically with the network size), so long as
the committed group constitutes more than about 10% of the population (with the
findings being qualitatively similar for sparse networks as well). Here we
study the more general case of opinion evolution when two groups committed to
distinct, competing opinions and , and constituting fractions and
of the total population respectively, are present in the network. We show
for stylized social networks (including Erd\H{o}s-R\'enyi random graphs and
Barab\'asi-Albert scale-free networks) that the phase diagram of this system in
parameter space consists of two regions, one where two stable
steady-states coexist, and the remaining where only a single stable
steady-state exists. These two regions are separated by two fold-bifurcation
(spinodal) lines which meet tangentially and terminate at a cusp (critical
point). We provide further insights to the phase diagram and to the nature of
the underlying phase transitions by investigating the model on infinite
(mean-field limit), finite complete graphs and finite sparse networks. For the
latter case, we also derive the scaling exponent associated with the
exponential growth of switching times as a function of the distance from the
critical point.Comment: 23 pages: 15 pages + 7 figures (main text), 8 pages + 1 figure + 1
table (supplementary info
Divide-and-rule policy in the Naming Game
The Naming Game is a classic model for studying the emergence and evolution
of language in a population. In this paper, we consider the Naming Game with
multiple committed opinions and investigate the dynamics of the game on a
complete graph with an arbitrary large population. The homogeneous mixing
condition enables us to use mean-field theory to analyze the opinion evolution
of the system. However, when the number of opinions increases, the number of
variables describing the system grows exponentially. We focus on a special
scenario where the largest group of committed agents competes with a motley of
committed groups, each of which is significantly smaller than the largest one,
while the majority of uncommitted agents initially hold one unique opinion. We
choose this scenario for two reasons. The first is that it arose many times in
different societies, while the second is that its complexity can be reduced by
merging all agents of small committed groups into a single committed group. We
show that the phase transition occurs when the group of the largest committed
fraction dominates the system, and the threshold for the size of the dominant
group at which this transition occurs depends on the size of the committed
group of the unified category. Further, we derive the general formula for the
multi-opinion evolution using a recursive approach. Finally, we use agent-based
simulations to reveal the opinion evolution in the random graphs. Our results
provide insights into the conditions under which the dominant opinion emerges
in a population and the factors that influence this process.Comment: 13 pages, 12 figure
An Analysis of the Matching Hypothesis in Networks
The matching hypothesis in social psychology claims that people are more
likely to form a committed relationship with someone equally attractive.
Previous works on stochastic models of human mate choice process indicate that
patterns supporting the matching hypothesis could occur even when similarity is
not the primary consideration in seeking partners. Yet, most if not all of
these works concentrate on fully-connected systems. Here we extend the analysis
to networks. Our results indicate that the correlation of the couple's
attractiveness grows monotonically with the increased average degree and
decreased degree diversity of the network. This correlation is lower in sparse
networks than in fully-connected systems, because in the former less attractive
individuals who find partners are likely to be coupled with ones who are more
attractive than them. The chance of failing to be matched decreases
exponentially with both the attractiveness and the degree. The matching
hypothesis may not hold when the degree-attractiveness correlation is present,
which can give rise to negative attractiveness correlation. Finally, we find
that the ratio between the number of matched couples and the size of the
maximum matching varies non-monotonically with the average degree of the
network. Our results reveal the role of network topology in the process of
human mate choice and bring insights into future investigations of different
matching processes in networks
A gentle introduction to the minimal Naming Game
Social conventions govern countless behaviors all of us engage in every day, from how we greet each other to the languages we speak. But how can shared conventions emerge spontaneously in the absence of a central coordinating authority? The Naming Game model shows that networks of locally interacting individuals can spontaneously self-organize to produce global coordination. Here, we provide a gentle introduction to the main features of the model, from the dynamics observed in homogeneously mixing populations to the role played by more complex social networks, and to how slight modifications of the basic interaction rules give origin to a richer phenomenology in which more conventions can co-exist indefinitely
Network resilience
Many systems on our planet are known to shift abruptly and irreversibly from
one state to another when they are forced across a "tipping point," such as
mass extinctions in ecological networks, cascading failures in infrastructure
systems, and social convention changes in human and animal networks. Such a
regime shift demonstrates a system's resilience that characterizes the ability
of a system to adjust its activity to retain its basic functionality in the
face of internal disturbances or external environmental changes. In the past 50
years, attention was almost exclusively given to low dimensional systems and
calibration of their resilience functions and indicators of early warning
signals without considerations for the interactions between the components.
Only in recent years, taking advantages of the network theory and lavish real
data sets, network scientists have directed their interest to the real-world
complex networked multidimensional systems and their resilience function and
early warning indicators. This report is devoted to a comprehensive review of
resilience function and regime shift of complex systems in different domains,
such as ecology, biology, social systems and infrastructure. We cover the
related research about empirical observations, experimental studies,
mathematical modeling, and theoretical analysis. We also discuss some ambiguous
definitions, such as robustness, resilience, and stability.Comment: Review chapter
Consensus Building by Committed Agents
One of the most striking features of our time is the polarization, nationally and globally, in politics and religion. How can a society achieve anything, let alone justice, when there are fundamental disagreements about what problems a society needs to address, about priorities among those problems, and no consensus on what constitutes justice itself? This paper explores a model for building social consensus in an ideologically divided community. Our model has three states: two of these represent ideological extremes while the third state designates a moderate position that blends aspects of the two extremes. Each individual in the community is in one of these three states. A constant fraction of individuals are committed agents dedicated to the third, moderate state, while all other moderates and those from either extreme are uncommitted. The states of the uncommitted may change as they interact, according to prescribed rules, at each time step with their neighbors; the committed agents, however, cannot be moved from their moderate position, although they can influence neighbors. Our main objective is to investigate how the proportion of committed agents affects the large-scale dynamics of the population: in other words, we examine the special role played by those committed to embracing both sides of an ideological divide. A secondary but equally important goal is to gently introduce important dynamical systems concepts in a natural setting. Finally, we briefly outline a model with different interaction rules, a fourth state representing those who loathe the other three states, and agents who may be committed to any one of the four states
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