Mitigation of adversarial attacks on voter model dynamics by network heterogeneity

Abstract

Voter model dynamics in complex networks are vulnerable to adversarial attacks. In particular, the voting outcome can be inverted by adding extremely small perturbations that are strategically generated in social networks, even when one opinion is dominant over the other. However, the mitigation of adversarial attacks on the voter model dynamics in complex networks has not been thoroughly investigated. Thus, we examined network structures that could mitigate adversarial attacks using model networks and real-world networks, considering that the network structure affects the voter model dynamics. Numerical simulations demonstrated that the heterogeneity of node degrees in the networks (degree heterogeneity) significantly mitigates adversarial attacks. In particular, for complex networks with a power-law degree distribution $P(k)\sim k^{-\gamma}$, the mitigation effect is significant for $\gamma \leq 3$. However, the mitigation effect of the degree heterogeneity was relatively weak for large and dense networks. The degree correlation and clustering in the networks exhibited almost no mitigation effect. The results enhance our understanding of how opinion dynamics and collective decision-making are distorted in social networks and may be useful for considering defense strategies against adversarial attacks.

Crossover phenomenon in adversarial attacks on voter model

“…n co ∼ ϵ −1/α . The theoretical findings of this study provide quantitative understanding of previous studies [19,21].…”

“…The relation n co ∼ ϵ −1/α suggests that for given networks of size perturbation ϵ to distort opinion dynamics in scale-free networks with degree exponent 2 < γ < exceeds that in non-scale-free networks because α = (γ − 1)/2 < 1 (figure 3). (Note that [21] has pointed out the tendency by numerical simulations.) Considering the heterogeneity of social interactions in most social media [24][25][26], this result is not unfavorable for users of such services.…”

“…In [19], which theoretically showed that an adversarial attack on voter dynamics can be realized efficiently, it was found that the voter dynamics in modeled and real-world complex networks are quickly distorted by the addition of small perturbations in computer simulations. In addition, [21] numerically found that degree inhomogeneity mitigates the effects of adversarial attacks on voter dynamics. In this study, we investigated adversarial attacks on the voter model in random networks, analytically obtaining the probability P +1 to distort the dynamics and the consensus time τ n for random networks with size n and a perturbation ϵ in the mean-field approximation.…”

“…This study only addressed adversarial attacks on the voter model in random networks. The effects of correlated structures, such as degree correlation, community structures, and higher-order structures, on this model, are left topics for future research as [21] has reported the impact of clustering and degree correlation in real-world networks. In addition, it is essential to investigate whether there are efficient ways to attack more complex opinion dynamics models that reflect reality and evaluate the network robustness against such attacks.…”

“…Thus, the voter dynamics of complex networks are quickly distorted by the introduction of small perturbations. Further, [21] focused on the effects of adversarial attacks on voter dynamics for different network structures. One of the primary conclusions was that degree inhomogeneity mitigates the effect of adversarial attacks on voter dynamics.…”