Decision-Making under Negativity Bias: Double Hysteresis in the Opinion-Dependent $q$-Voter Model

TL;DR

This paper introduces an opinion-dependent $q$-voter model capturing negativity bias, revealing complex collective behaviors like double hysteresis and irreversibility, which have implications for understanding market stability and reputation dynamics.

Contribution

It generalizes the $q$-voter model with opinion-dependent influence groups, uncovering new phenomena such as double hysteresis and path-dependent opinion dynamics.

Findings

Discontinuous phase transitions observed in the model.

Double hysteresis phenomena identified, including irreversible cases.

Model explains how negativity bias can cause lasting opinion shifts.

Abstract

Negative information often exerts a disproportionately strong impact on human decision-making, a phenomenon known as the negativity bias. In behavioral economics, this effect is formally captured by Prospect Theory, which posits that losses loom larger than equivalent gains. For example, a single negative product review can outweigh numerous positive ones, reflecting this principle of loss aversion in consumer behavior. While this psychological effect has been widely documented, its implications for collective opinion dynamics, critical for understanding market stability and reputation dynamics, remain poorly understood. Here, we generalize the $q$-voter model with independence by introducing opinion-dependent influence group sizes, $q_+$ and $q_-$, which represent the social reinforcement needed to change an opinion from negative to positive and from positive to negative, respectively. We study two versions of this asymmetric model: a baseline model that reduces to the standard $q$-voter model when $q_+ = q_- = q$, and an extended model that incorporates an additional asymmetry expressed as a preference for one opinion. In its reduced version, this represents a minimal model in terms of non-linearity within the $q$-voter framework that allows for discontinuous phase transitions and hysteresis. Using mean-field analysis and computer simulations, we show that these modifications lead to rich collective behaviors, including double hysteresis, one form of which is irreversible, providing a mechanism for path-dependence and the sustained, irrecoverable damage to collective sentiment, brand equity, or market confidence.