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

Oriol Artime1,2, Adrián Carro3,4, Antonio F. Peralta1, José J. Ramasco1, Maxi San Miguel1 and Raúl Toral1

1Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, Spain.
2 Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo (TN), Italy.
3 Institute for New Economic Thinking at the Oxford Martin School, University of Oxford, OX2 6ED Oxford, UK.
4 Mathematical Institute, University of Oxford, OX2 6GG Oxford, UK.

(December 2018)

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.