Democratic Resilience and Sociotechnical Shocks

TL;DR

The paper develops a threshold-based dynamic model of civic-network attrition under harassment and disinformation to study democratic resilience. It introduces a systemic resilience metric $R(F)$ that links macro robustness to micro-level harassment thresholds via the threshold distribution's quantile function $Q = F^{-1}$, and extends the model to include recruitment, infiltration, and targeted harassment. It shows how adversaries can optimize harassment policies and how interventions using optimal transport (Wasserstein distance) can shift $F$ to more resilient distributions within a budget. The results highlight conditions under which catastrophic unraveling occurs and provide a quantitative framework for policy design to retain officials and boost turnout, with implications for other civic infrastructures. These insights offer a principled bridge between micro-level heterogeneity, sociotechnical shocks, and macro-level democratic resilience in the information age.

Abstract

We focus on the potential fragility of democratic elections given modern information-communication technologies (ICT) in the Web 2.0 era. Our work provides an explanation for the cascading attrition of public officials recently in the United States and offers potential policy interventions from a dynamic system's perspective. We propose that micro-level heterogeneity across individuals within crucial institutions leads to vulnerabilities of election support systems at the macro scale. Our analysis provides comparative statistics to measure the fragility of systems against targeted harassment, disinformation campaigns, and other adversarial manipulations that are now cheaper to scale and deploy. Our analysis also informs policy interventions that seek to retain public officials and increase voter turnout. We show how limited resources (for example, salary incentives to public officials and targeted interventions to increase voter turnout) can be allocated at the population level to improve these outcomes and maximally enhance democratic resilience. On the one hand, structural and individual heterogeneity cause systemic fragility that adversarial actors can exploit, but also provide opportunities for effective interventions that offer significant global improvements from limited and localized actions.

Figures (2)

• Figure 1: We plot $p_{\infty}(H)$ as a function of $H$ for $F_1 \sim \hbox{Uniform}[0, 1]$ in red, $F_2 \sim \hbox{Exponential}(1)$ in blue, whose corresponding resilience are $1/4$ and $1/e$, respectively. Note the stochastic dominance relationship between these distributions: $F_2 \succ F_1$ which is reflected in their resilience metrics: $\mathcal{R}(F_2) = {1}/{e} > \mathcal{R}(F_1) = {1}/{4}$. We can compute $\mathcal{R}(F)$ explicitly as a function of distribution parameters, for example, $\mathcal{R}(F) = b^2/(4(b-a))$ for $\theta \sim \hbox{Uniform}[a, b]$, whereas for exponential distribution $\mathcal{R}(F) = 1/(e \lambda)$ for $\theta \sim \hbox{Exp}(\lambda)$. One may look into the entirety of the $p_\infty(H)$ plot and use more nuanced statistics to better distinguish different distributions. For example, the area under the curve (AUC) of $p_\infty(H)$ over a fixed range, $[H_{\min},H_{\max}]$, can give a more refined characterization of resilience and be used as an alternative metric: $\int_{H_{\min}}^{H_{\max}}p_\infty(H)dH$. One particular value of interest would be $p_{\infty}(\mathcal{R}(F))$: the fraction remaining in the system at the critical harassment value $\mathcal{R}(F)$.
• Figure 2: We plot $\mathcal{R}_{\alpha,\lambda}(\hbox{Uniform}[0, 1])$ as a function of recruitment parameter $\alpha$ and infiltration $\lambda$. As $\alpha \to 0$, the local administration is perfectly able to replace departing officials and resilience converges to its maximum value of one corresponding to the upper support of the $\hbox{Uniform}[0, 1]$ threshold distributions. As $\alpha \to 1$ and for larger values of $\lambda$ the resilience is zero; the system becomes completely fragile and faces complete unraveling with any input harassment $H>0$.

Theorems & Definitions (11)

• Proposition 1: Monotonicity and Convergence
• Definition 1: Resilience
• Theorem 2: Resilience and Quantile Function
• Proposition 3: A Stochastic Ordering
• Proposition 4
• Proposition 5
• Proposition 6
• proof
• proof
• proof