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Register a new userBounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions
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In this work we study the coupled dynamics of social balance and opinion formation. We propose a model where agents form opinions under bounded confidence, but only considering the opinions of their friends. The signs of social ties -friendships and enmities- evolve seeking for social balance, taking into account how similar agents opinions are. We consider both the case where opinions have one and two dimensions. We find that our dynamics produces the segregation of agents into two cliques, with the opinions of agents in one clique differing from those in the other. Depending on the level of bounded confidence, the dynamics can produce either consensus of opinions within each clique or the coexistence of several opinion clusters in a clique. For the uni-dimensional case, the opinions in one clique are all below the opinions in the other clique, hence defining a left clique and a right clique. In the two-dimensional case, our numerical results suggest that the two cliques are separated by a hyperplane in the opinion space. We also show that the phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the context of politics, we comment about the possible relation of our results to the fragmentation of an ideology and the emergence of new political parties.
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We present a model for studying communities of epistemically interacting agents who update their belief states by averaging (in a specified way) the belief states of other agents in the community. The agents in our model have a rich belief state, involving multiple independent issues which are interrelated in such a way that they form a theory of the world. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating (in the given way). To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. It is shown that, under the assumptions of our model, an agent always has a probability of less than 2% of ending up in an inconsistent belief state. Moreover, this probability can be made arbitrarily small by increasing the number of independent issues the agents have to judge or by increasing the group size. A real-world situation to which this model applies is a group of experts participating in a Delphi-study.
Social groups with widely different music tastes, political convictions, and religious beliefs emerge and disappear on scales from extreme subcultures to mainstream mass-cultures. Both the underlying social structure and the formation of opinions are dynamic and changes in one affect the other. Several positive feedback mechanisms have been proposed to drive the diversity in social and economic systems, but little effort has been devoted to pinpoint the interplay between a dynamically changing social network and the spread and gathering of information on the network. Here we analyze this phenomenon in terms of a social network-model that explicitly simulates the feedback between information assembly and emergence of social structures: changing beliefs are coupled to changing relationships because agents self-organize a dynamic network to facilitate their hunter-gatherer behavior in information space. Our analysis demonstrates that tribal organizations and modular social networks can emerge as a result of contact-seeking agents that reinforce their beliefs among like-minded. We also find that prestigious persons can streamline the social network into hierarchical structures around themselves.
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,ldots$, with probability $pi_1>0$ a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability $pi_2$ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability $pi_3=1-pi_1-pi_2<1/2$ a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction $p_k$ of vertices with degree $k$, and solving this recursion reveals that, for $pi_3<1/3$, we have $p_ksim k^{-(3-7pi_3)/(1-3pi_3)}$, while, for $pi_3>1/3$, the fraction $p_k$ decays exponentially at rate $(pi_1+pi_2)/2pi_3$. There is hence a non-trivial upper bound for how much deletion the network can incorporate without loosing the power-law behavior of the degree distribution. The analytical results are supported by simulations.
The communication process in a situation of emergency is discussed within the Scheff theory of shame and pride. The communication involves messages from media and from other persons. Three strategies are considered: selfish (to contact friends), collective (to join other people) and passive (to do nothing). We show that the pure selfish strategy cannot be evolutionarily stable. The main result is that the community structure is statistically meaningful only if the interpersonal communication is weak.
In recent numerical and analytical studies, Rabbani {it et al.} [Phys. Rev. E {bf 99}, 062302 (2019)] observed the first-order phase transition in social triads dynamics on complete graph with $N=50$ nodes. With Metropolis algorithm they found critical temperature on such graph equal to 26.2. In this comment we extend their main observation in more compact and natural manner. In contrast to the commented paper we estimate critical temperature $T^c$ for complete graph not only with $N=50$ nodes but for any size of the system. We have derived formula for critical temperature $T^c=(N-2)/a^c$, where $N$ is the number of graph nodes and $a^capprox 1.71649$ comes from combination of heat-bath and mean-field approximation. Our computer simulation based on heat-bath algorithm confirm our analytical results and recover critical temperature $T^c$ obtained earlier also for $N=50$ and for systems with other sizes. Additionally, we have identified---not observed in commented paper---phase of the system, where the mean value of links is zero but the system energy is minimal since the network contains only balanced triangles with all positive links or with two negative links. Such a phase corresponds to dividing the set of agents into two coexisting hostile groups and it exists only in low temperatures.
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