The influence of an individual opinion in the Sznajd Model

TL;DR

This paper investigates how a single individual's opinion change affects consensus in the Sznajd Model using Damage Spreading, revealing limited influence, effects on consensus timing, and observed scaling laws.

Contribution

It introduces a Damage Spreading approach to quantify the influence of one person's opinion change within the Sznajd Model, highlighting its limited but measurable impact.

Findings

The influence of one person rarely changes the overall consensus.

Opinion change effects diminish over time and space, following power laws.

Consensus times can be delayed or accelerated by a single opinion change.

Abstract

The method of Damage Spreading was used to simulate the influence that a single persons' change of opionion has on the consensus opinion built up in a population if one assumes opinions to form according to the Sznajd Model. The results confirm the intuitive assumption that there is hardly any chance for one person to change the consensus, that the effect of this change dies out after a certain time and its range decreases with time. The consensus times were compared and it turned out that the consensus can be delayed or accelerated by this slight modification and that the amount of the difference in the consensus times obeys a certain power law as well as the lifetime of the effect. Moreover two scaling laws concerning temporal and spatial aspects could be observed up to a certain size of population.