Competition among reputations in the 2D Sznajd model: Spontaneous emergence of democratic states

TL;DR

This paper introduces a reputation mechanism into the 2D Sznajd model, preventing full consensus and leading to the spontaneous emergence of democratic states, with different dynamics depending on how reputation is updated.

Contribution

It presents a novel modification to the Sznajd model by incorporating reputation scores, revealing how this affects consensus formation and phase transitions.

Findings

Reputation prevents full consensus across a wide parameter range.

Relaxation times follow a log-normal-like distribution, larger when reputation can decrease.

Phase transition depends on initial opinion density, with different critical points in two cases.

Abstract

We propose a modification in the Sznajd sociophysics model defined on the square lattice. For this purpose, we consider reputation-a mechanism limiting the agents' persuasive power. The reputation is introduced as a time-dependent score, which can be positive or negative. This mechanism avoids dictatorship (full consensus, all spins parallel) for a wide range of model parameters. We consider two different situations: case 1, in which the agents' reputation increases for each persuaded neighbor, and case 2, in which the agents' reputation increases for each persuasion and decreases when a neighbor keeps his opinion. Our results show that the introduction of reputation avoids full consensus even for initial densities of up spins greater than 1/2. The relaxation times follow a log-normal-like distribution in both cases, but they are larger in case 2 due to the competition among reputations. In addition, we show that the usual phase transition occurs and depends on the initial concentration $d$ of individuals with the same opinion, but the critical points $d_{c}$ in the two cases are different.