Damage Spreading, Coarsening Dynamics and Distribution of Political Votes in Sznajd Model on Square Lattice

Abstract

In the Sznajd model of sociophysics on the square lattice, neighbors having the same opinion convince their neighbors of this opinion. We study scaling of the cluster growth. The spreading-of-damage technique is applied for the spread of opinions. We study the time evolution of the damage and compare it with the magnetization evolution. We also compare this model with the Ising model at low temperatures. It was recently shown that the distribution of votes in Brazilian elections follows a power law behavior with exponent ≃ -1.0. A model for elections based on the Sznajd model is proposed. The exponent obtained for the distribution of votes during the transient agrees with that obtained for elections.

Statistical Properties of the Proportional Voting Process

“…Similar research has also been done on the results from few other countries and resembling results were obtained [4][5][6]. In this paper we show that results of Polish elections have a log-normal distribution.…”

How to Convince Others? Monte Carlo Simulations of the Sznajd Model

“…This phase transition at p c = 1/2 does not exist in one dimension [11] or when a single site (instead of a pair or plaquette) on the square lattice [19] already convinces its neighbours. Pictures and cluster analysis of the domain formation process [20,12] show strong similarity with Ising models. The time needed to reach a complete consensus fluctuates widely and (in the cases were a phase transition is found) does not follow a Gaussian or log-normal distribution.…”

“…Talking about voting, the results of Brazilian elections (distribution of number of votes among many candidates) were reproduced quite well if the Sznajd model with many different opinions (instead of only ±1) is put on a Barabási-Albert network [20,32]. If the Sznajd dynamics is simultaneous to the growth of this network, complete consensus no longer is possible [33].…”

Majority versus minority dynamics: Phase transition in an interacting two-state spin system

“…Such a rule naturally leads to eventual global consensus except in the anomalous case of an antiferromagnetic initial state. The generic questions posed above about opinion evolution in the MM model are also of basic interest in the Sznajd model [9] and considerable work has recently appeared to quantify its basic properties [9,10,11,12,13]. There is also a wide variety of kinetic spin models of social interactions that incorporate, for example, multiple traits [14], incompatibility [15,16], and other relevant features [17].…”