Why can’t we go back to paradise?

Abstract

According to the structural balance theory a social network is in an equilibrium state when it is divided into two communities and there are friendly links inside communities and hostile links between them. Then rules “friend of my friend is my friend” and “enemy of my friend is my enemy” etc are fulfilled. Such a configuration corresponds to the social polarization and can be a result (for example) of segregating ideologies or opposing interests existing in both communities. A social equilibrium can exist also as a “paradise” state when only friendship links exist. The paradise state is however rarely observed and during the lecture I will discuss possible reasons for this.

The first example will be the case when social agents do not possess any attributes but connecting links are binary variables that are described by Ising model with three spins interactions and the system is in a thermal bath corresponding to a social noise. Then if an initial state consists of all positive links, the paradise state can be preserved provided the level of this noise is below some critical value. When crossing the critical point, one observes a discontinuous and irreversible phase to a disordered and unbalanced state with the equal number of positive and negative links but without a division into two hostile cliques. When initial conditions for links polarities are random then for low values of social noise there is a bipolar state of two mutually hostile cliques [1].

The second example will be the case when every agent possesses G attributes, they can evolve in time to obey rules of the structural balance. Then for the group of N agents the paradise state can appear only if G > O(N2) and when the parameter describing the willingness for consensus is high enough. When these conditions are not met then the system stays in quasi-stationary states that can be far from the paradise [2].

I will show also that effects of the structural balance in a data set received from the NetSense experiment are empirically measurable when signs of edges are defined by multidimensional differences between opinions on all topics. Yet, when these signs are defined by a difference between opinions on each topic separately, the triadic interactions’ influence is indistinguishable from noise [3].
Finally, a general model for how attributes can reduce polarization in social groups will be studied and it will be shown that the while it is easier to prevent than to destabilize polarization, we find that usually the most effective at both are continuous attributes, followed by ordered attributes and, finally, binary attributes [4]. References

Relevant publications

[1] Mean-field approximation for structural balance dynamics in heat bath, K Malarz, J.A Hołyst, Physical Review E 106 (6), 064139 (2022)

[2] Homophily based on few attributes can impede structural balance, P.J Górski, K Bochenina, J.A Hołyst, RM D’Souza, Physical Review Letters 125 (7), 078302 (2020)

[3] Multidimensional attributes expose Heider balance, dynamics to measurements J. Linczuk, P.J. Górski, B.K. Szymanski, and J.A. Hołyst, submitted (2023)

[4] A general model for how attributes can reduce polarization in social groups, P.J. Górski, C. Atkisson, J.A. Hołyst, Network Science, 1-24 (2023).