Stable target opinion through power-law bias in information exchange

We study a model of binary decision making when a certain population of agents is initially seeded with two different opinions, “+” and “−,” with fractions p1 and p2, respectively, p1+p2=1. Individuals can reverse their initial opinion only once based on this information exchange. We study this model on a completely connected network, where any pair of agents can exchange information, and a two-dimensional square lattice with periodic boundary conditions, where information exchange is possible only between the nearest neighbors. We propose a model in which each agent maintains two counters of opposite opinions and accepts opinions of other agents with a power-law bias until a threshold is reached, when they fix their final opinion. Our model is inspired by the study of negativity bias and positive-negative asymmetry, which has been known in the psychology literature for a long time. Our model can achieve a stable intermediate mix of positive and negative opinions in a population. In particular, we show that it is possible to achieve close to any fraction p3, 0≤p3≤1, of “−” opinion starting from an initial fraction p1 of “−” opinion by applying a bias through adjusting the power-law exponent of p3.