arXiv subjects

Piotr Gronek

Publications and source records attributed to Piotr Gronek.

5 recordsLinked to original sources

arXiv2019

The Heider balance and the looking-glass self

We consider the dynamics of interpersonal relations which leads to balanced states in a fully connected network. Here this approach is applied to directed networks with asymmetric relations, and it is generalized to include self-evaluation of actors, according to the 'looking-glass self' theory. A new index of self-acceptance is proposed: the relation of an actor to him/herself is positive, if the majority of his/her positive relations to others are reciprocated. Sets of stable configurations of relations are obtained under the dynamics, where the self-evaluation of some actors is negative. Within each set all configurations have the same structure.

physics.soc-ph↗

arXiv2017

Paradox of integration - mean field approach

Recently a computational model has been proposed of the social integration, as described in sociological terms by Peter Blau. In this model, actors praise or critique each other, and these actions influence their social status and raise negative or positive emotions. The role of a self-deprecating strategy of actors with high social status has also been discussed there. Here we develop a mean field approach, where the active and passive roles (praising and being praised, etc.) are decoupled. The phase transition from friendly to hostile emotions has been reproduced, similarly to the previously applied purely computational approach. For both phases, we investigate the time dependence of the distribution of social status. There we observe a diffusive spread, which - after some transient time - appears to be limited from below or from above, depending on the phase. As a consequence, the mean status flows.

physics.soc-ph↗

arXiv2013

How many parameters to model states of mind ?

A series of examples of computational models is provided, where the model aim is to interpret numerical results in terms of internal states of agents minds. Two opposite strategies or research can be distinguished in the literature. First is to reproduce the richness and complexity of real world as faithfully as possible, second is to apply simple assumptions and check the results in depth. As a rule, the results of the latter method agree only qualitatively with some stylized facts. The price we pay for more detailed predictions within the former method is that consequences of the rich set of underlying assumptions remain unchecked. Here we argue that for computational reasons, complex models with many parameters are less suitable.

physics.soc-ph↗

arXiv2010

Zaller-Deffuant model of mass opinion

Recent formulation of the Zaller model of mass opinion is generalized to include the interaction between agents. The mechanism of interaction is close to the bounded confidence model. The outcome of the simulation is the probability distribution of opinions on a given issue as dependent on the mental capacity of agents. Former result was that a small capacity leads to a strong belief. Here we show that an intensive interaction between agents also leads to a consensus, accepted without doubts.

physics.soc-ph↗

arXiv2005

The Heider balance - a continuous approach

The Heider balance (HB) is investigated in a fully connected graph of $N$ nodes. The links are described by a real symmetric array r(i,j), i,j=1,...,N. In a social group, nodes represent group members and links represent relations between them, positive (friendly) or negative (hostile). At the balanced state, r(i,j)r(j,k)r(k,i)>0 for all the triads (i,j,k). As follows from the structure theorem of Cartwright and Harary, at this state the group is divided into two subgroups, with friendly internal relations and hostile relations between the subgroups. Here the system dynamics is proposed to be determined by a set of differential equations. The form of equations guarantees that once HB is reached, it persists. Also, for N=3 the dynamics reproduces properly the tendency of the system to the balanced state. The equations are solved numerically. Initially, r(i,j) are random numbers distributed around zero with a symmetric uniform distribution of unit width. Calculations up to N=500 show that HB is always reached. Time to get the balanced state varies with the system size N as N^{-1/2}. The spectrum of relations, initially narrow, gets very wide near HB. This means that the relations are strongly polarized. In our calculations, the relations are limited to a given range around zero. With this limitation, our results can be helpful in an interpretation of somestatistical data.

physics.soc-ph↗