Who is left, who is right?

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Abstract

We propose a model to simulate the process of opinion formation in a society where the traditional division into leftists and rightists is not enough any longer. The model is based on the Ashkin–Teller idea to assign two Ising spins to each site (agent). The two states (up and down) of the first spin represent two possible opinions on any question in an economic area, and the two states of the second spin in a personal area. We assume that the mechanisms of opinion formation in both of these areas are different. The interaction between them is introduced in the form of a tolerance factor. It has been found, among others, that the formation of consensus between groups of agents which differ only in the economic area is quite simple, whereas if they differ in the personal area no consensus is possible.

Introduction

Modern societies rely heavily on a group decision, but the part of what makes for healthy communities is a sense that all members feel being heard. That is why finding consensus is very important in many branches of social life. Recently both sociologists [1], [2], [3], [4] and physicists [5], [6], [7], [8], [9], [10], [11], [12] tried to find out when (in computer simulation) a complete consensus from initially diverging opinions emerges.

Recently we have proposed a simple model [13] to describe how opinions spread in human society. The crucial difference of our model compared to voter or Ising-type models is that information flows outward [14]. In our model each site of a one-dimensional lattice carries an Ising spin. Two neighboring parallel spins—i.e., two neighboring people sharing the same opinion—convince their neighbors of this opinion. If they do not have the same opinion, they bring their neighbors to the opposite position. The motivation to propose this new dynamics was a phenomenon called by social psychologists “social validation”—one fundamental way that we decide what to do in a situation is to look to what others are doing. An isolated person does not convince others; a group of people sharing the same opinion influences the neighbors much more easily. Our model, named by Stauffer the “Sznajd model” (SM), has been modified and applied in sociology, marketing, finance, and politics; for reviews see Stauffer [14] and Schechter [15].

Section snippets

Modern political attitudes—beyond left and right

It is very common to talk about left and right wings in politics. Left-wing, political left, or simply the left are terms which refer to the segment of the political spectrum typically associated with any of several strains of socialism, social democracy, or liberalism. On the other hand, right-wing, political right, or simply the right are terms which refer to the segment of the political spectrum typically associated with conservatism.

It has often been pointed out that the terms “right” and

Model

Each person is characterized by two traits ( σ i , S i ) , where σ i describes the attitude to personal freedom and S i describes the attitude to economic freedom. Both traits are represented by Ising spins, i.e., binary variables (like in the Ashkin–Teller model [23]). This representation is simply a discretization of the diagram presented in Fig. 1. Thus in our authoritarian–conservative–libertarian–socialist (ACLS) model, like in reality, we have four types of political attitudes:

  • (1)

    Authoritarians: ( σ i = -

Consensus formation

Social relations should be represented by networks instead of lattices [24]. However, we hope that the main features of opinion dynamics can be analyzed on a square lattice which is, of course, a better approximation for social interactions than the chain considered in the previous section. The first generalization of SM to the square lattice was done by Stauffer et al. [20]. In fact, they proposed six different generalizations, but here we will use only one of them (rule Ia). A 2 × 2 plaquette

Summary

We have introduced and studied a model of opinion formation in a society which cannot be divided into traditional two wings, left and right. There have been various attempts to find a replacement for such a division, and one of the possibilities is the so-called political compass [18]. The political compass works by separating ideology into two major areas: economic and personal. The affiliation to one of the four clusters of the political attitude is connected with the role of the government

Acknowledgements

The authors are grateful to Dietrich Stauffer to whom this paper is dedicated, for his pains to propagate statistical physics models to fields outside physics.

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