# Herding and idiosyncratic choices: Nonlinearity and aging-induced transitions in the noisy voter model

## TL;DR

This paper investigates how nonlinear interactions and aging effects in the noisy voter model create a robust herding to non-herding transition, which is otherwise finite-size and disappears as the population grows.

## Contribution

It introduces two mechanisms—nonlinear interactions and aging—that stabilize the herding transition in the noisy voter model, making it well-defined for large populations.

## Key findings

- Nonlinear interactions induce a robust herding transition.
- Aging effects reinforce the stability of the transition.
- The transition persists in large populations due to these mechanisms.

## Abstract

We consider the herding to non-herding transition caused by idiosyncratic choices or imperfect imitation in the context of the Kirman Model for financial markets, or equivalently the Noisy Voter Model for opinion formation. In these original models this is a finite size transition that disappears for a large number of agents. We show how the introduction of two different mechanisms make this transition robust and well defined. A first mechanism is nonlinear interactions among agents taking into account the nonlinear effect of local majorities. The second one is aging, so that the longer an agent has been in a given state the more reluctant she becomes to change state.