Complete aging in the noisy voter model enhances consensus formation

TL;DR

This paper explores how complete aging in the noisy voter model influences consensus formation, showing that aging enhances consensus but can prevent steady states when aging probability diminishes over time.

Contribution

It introduces a comprehensive aging scenario affecting both herding and idiosyncratic behaviors, with analytical and simulation validation showing enhanced consensus effects.

Findings

Complete aging shifts the critical point to higher values.

Aging enhances consensus formation.

Steady states may not form when aging probability decays to zero.

Abstract

We investigate the effects of aging in the noisy voter model considering that the probability to change states decays algebraically with age $\tau$, defined as the time elapsed since adopting the current state. We study the complete aging scenario, which incorporates aging to both mechanisms of interaction: herding and idiosyncratic behavior, and compare it with the partial aging case, where aging affects only the herding mechanism. Analytical mean-field equations are derived, finding excellent agreement with agent-based simulations on a complete graph. We observe that complete aging enhances consensus formation, shifting the critical point to higher values compared to the partial aging case. However, when the aging probability decays asymptotically to zero for large $\tau$, a steady state is not always attained for complete aging.