Stable target opinion through power law bias in information exchange

TL;DR

This paper introduces a model of binary decision-making influenced by power law bias, demonstrating how stable mixed opinions can be achieved in a population through information exchange on different network structures.

Contribution

It proposes a novel opinion dynamics model incorporating power law bias and thresholds, inspired by psychological negativity bias, to explain stable mixed opinions.

Findings

Stable intermediate opinion mixtures are achievable.

Adjusting the power law bias controls the final opinion distribution.

The model applies to both fully connected and lattice networks.

Abstract

We study a model of binary decision making when a certain population of agents is initially seeded with two different opinions, `$+$' and `$-$', with fractions $p_1$ and $p_2$ respectively, $p_1+p_2=1$. 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 known in the psychology literature for a long time. Our model can achieve 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 $p_3, 0\leq p_3\leq 1$, of `$-$' opinion starting from an initial fraction $p_1$ of `$-$' opinion by applying a bias through adjusting the power law exponent of $p_3$.