Asynchronous expressed-private $q$-voter model on networks: self-anticonformity and preference falsification

TL;DR

The paper investigates how asynchronous updates between private and expressed opinions influence collective dynamics in a dual-layer q-voter EPO framework, focusing on preference falsification and the intention–behavior gap. It introduces two α-EPO variants, with and without self-anticonformity, and analyzes their behavior on complete graphs, synthetic networks, and empirical organizational networks using Monte Carlo simulations, mean-field theory, and pair-approximation. Key findings show that self-anticonformity yields α-robust agreement and increases dissonance while leaving the macroscopic state unchanged for $0<\alpha<1$, whereas the non-anticonformity variant makes the order–disorder transition depend on $\alpha$ and can suppress hysteresis for $q=3$ above a critical $\alpha^*$. These insights have practical implications for managing public stance and timely collective responses in organizations and societies, suggesting strategies to encourage dissent and moderate public volatility might promote faster, more reliable norm adaptation.

Abstract

People may express preferences that differ from their privately held views, often under social pressure, and may fail to act on their stated intentions. Such inconsistencies are referred to as preference falsification and the intention-behavior gap, respectively. Both hamper collective decision-making and adaptation, complicating policy formulation and implementation. To simulate these phenomena, dual-layer opinion agent-based models are used, in which each agent holds both a private and an expressed (public) opinion. Within the $q$-voter framework, two expressed-private opinion (EPO) models have been introduced in which private and expressed opinions are updated synchronously; two variants differ only by the presence of self-anticonformity, a mechanism in which an agent may set its private opinion opposite to its current expressed opinion, breaking internal harmony and creating a state akin to cognitive dissonance. Here, we extend these models by introducing an asynchronous update: in each elementary step, an agent updates its private opinion with probability $α$ or its expressed opinion with complementary probability; hence the name $α$-EPO models. Using Monte Carlo simulations on both artificial and real organizational social networks, along with mean-field and pair approximation analyses, we show that self-anticonformity makes collective outcomes robust to behavioral volatility tuned by $α$, enhances collective agreement, and suppresses hysteresis. In contrast, without self-anticonformity, $α$ affects the nature of the transition between agreement and disagreement: higher values of $α$ suppress hysteresis and enhance overall agreement.

Figures (5)

• Figure 1: Visualization of a single update in the models with and without self-anticonformity (see the description directly above the bottom row in the left panel), for the case in which the focal agent is in harmony before the update.
• Figure 2: Visualization of a single update in the models with and without self-anticonformity (see the description directly above the bottom row in the left panel), for the case in which the focal agent is in dissonance before the update.
• Figure 3: Stationary concentrations of positive opinions at public level $c_S$ (left column), private level $c_\sigma$ (middle column) and dissonance $d$ (right column) as a function of the probability of independence $p$ obtained from mean field approximation with influence group of size $q = 3$. Rows correspond to different variants of the model: with (upper row) and without (bottom row) self-anticonformity. Results for $\alpha \in \{0.1,0.2,\ldots,0.9\}$ are shown, and the line color becomes more intense with increasing $\alpha$, i.e., the darker the line, the larger $\alpha$. In the upper row, the results for all values of $\alpha$ collapse onto the same curves for $c_S$ and $c_{\sigma}$; therefore, only a single line is visible.
• Figure 4: Dependence of lower $p^*_{low}$ (dotted lines) and upper $p^*_{up}$ (dashed lines) spinodals on $\alpha$ obtained from pair approximation. Results are shown for both variants of the EPO model, with (top row) and without (bottom row) self-anticonformity, obtained within the pair approximation for networks with average degree $k=15$ (left column), $k=50$ (middle column), and $k=150$ (right column).
• Figure 5: Stationary concentration of positive expressed opinions $c_S$ as a function of the independence probability $p$ for $\alpha=0.1, q = 3$. Monte Carlo results on empirical networks fire_organization_2016 are compared with simulations on Watts--Strogatz networks matched in size, average degree, and clustering coefficient (panels a, b, d, e). Panels (c, f) show simulations on random graphs of size $N = 10^4$ with average degree $k=15,50,150$. Full markers correspond to ordered initial conditions, while empty markers correspond to random initial conditions. Simulations results are compared with the pair-approximation prediction. Results are shown for both model variants: with (top row) and without (bottom row) self-anticonformity.