David Sabin-Miller's Papers

Political Opinion Dynamics Framework Proof-of-concept: Published at Physical Review Research or arXiv

This work establishes a modular data-informable theoretical framework for political opinion dynamics, focusing on leading-order "us vs them" reaction dynamics (local attraction, distal repulsion to politically charged experiences) coupled to a systematic bias in political information diets across the ideological spectrum. With some basic assumptions, the framework reproduces both realistic ideology distributions in equilibrium, and perturbation dynamics in line with empirical research. More importantly, this framework is built to admit messy real-world distributions in place of all assumed parameters and functional forms. One key innovation is the use of (systematically biased) probability distributions in place of explicit network structure for political influences, dramatically lightening the burden of data-gathering---this reflects an increasingly shared algorithmically-mediated information environment rather than one where local idiosyncracies dominate influence.

Interpreting Generalized Langevin Equations: arXiv

This work proposes a mathematically self-consistent interpretation of stochastic systems with random events "baked in" to nonlinear functions, which has previously been ill-defined. This need arose in the opinion-dynamics model above, which sought a continuous-time limit of a dynamical process driven by randomly generated influences, each having a nonlinear effect. Simple numerical simulation of such a system merely converges to deterministic (mean) behavior with smaller time-steps, yet these real-world processes exhibit stochastic trajectories in practice, so seeking a continuous-time stochastic limit required a choice of "drift" and "diffusion" terms which would allow a continuous-time model to match observed finite-time trajectory variance. The proposal is simply to utilize the mean and standard deviation of the transformed "random variable" (at the theoretical time-step level) as the drift and diffusion terms of a standard Ito SDE. This work then demonstrates the distinct implications of this process for the one-dimensional velocity distribution of a mesoscale particle in a rapidly-varying turbulent fluid in a quadratic-drag regime.

Equilibrium Analysis of Ito SDEs: arXiv

This work proposes a technique for interrogating the equilibria of Ito SDEs which do not admit exact solutions. This technique is inspired by a Master equation applied to an arbitrary-time-step numerical simulation of the system, which (for polynomial drift and diffusion terms) leads to a relationship between even raw moments of the equilibrium of such a process. This analysis also naturally yields a test for divergence of these moments, which may be impractical to observe in any finite-domain simulation. We provide evidence that these relationships appear to hold for one example system, which transitions from a near-Gaussian equilibrium to one with a divergent second moment as a parameter increases.

Coupled Particles: Published at Chaos or arXiv

This paper explores the behavior of particles on a one-dimensional domain coupled via an unusual potential-surface: a "Mexican Hat"-shaped function (the Ricker wavelet) which exhibits a "preferred distance" between long-range attraction and short-range repulsion, but in which that short-range repulsion weakens to indifference when particles stack perfectly upon one another. This combination of effects leads to complex self-organizing behavior when these particles are confined/"squeezed" together by a quadratic background potential of varying severity. We observe and analyze the emergence of simplicity: for large populations of particles, macroscopic behavior "converges" to a relatively simple paradigm of a few "major" bifurcations. We also briefly investigate a coupled-oscillators paradigm with this potential, and observe an intriguing proclivity for glass-like "frozen disorder" when these particles are overstuffed on a periodic domain, but we leave further analysis of that phenomenon to future work.

Post-doctoral Work

Collection of insights about the political spectrum: arXiv (Under review for publication at PLoS One)

This work introduces a medium-scale political survey on an age/sex/ethnicity/ideology-representative sample from the Prolific platform, and presents some broadly interesting patterns visible from the results. These speak to longstanding social-science questions about the robustness of the concept of ideology (comparing different measures of ideology), the relationship of ideology to political party affiliation, the (surprising lack of) ideological bias in interpreting the ideological spectrum itself, and more. Results from a non-representative sample of volunteers and Mechanical Turk "Masters" are included as a supplement, which provides additional support by reproducing all major effects.

Visualization of all statement-results from the 2024 survey: pdf

This paper displays some patterns of agreement/disagreement to the full slate of political statements from the survey. The visualization chosen allows the observation of all actual data points (the ideology and political party affiliation of the observer, and their agreement with the statement), along with some summarizing moving-median and 25/75th percentile trendlines for broad takeaways at a glance.

Data-driven model of US Information-Ideological dynamics: arXiv

This work publishes the robust population-level patterns in political reaction (proxied by agreement) and information exposure from the survey (its main purpose by design), then replaces all assumed parameters and functional forms from the original framework paper with those distributions. We then explore different dynamical hypotheses for translating these observable variables into actual induced ideological motion; the simplest model (motion = agreement * dissonance) predicts hyper-polarization under the observed data, so we then introduce a few additional conjectured psychological effects which yield more moderated, realistic ideology distributions, thus representing a new plausible model---to be investigated and/or replaced by future data-gathering efforts, gradually cornering our uncertainty and proposing additional theoretical complexity only when simpler models are falsified in this manner (and when it can be beholden to realistically attainable data). This work thus demonstrates a scientific feedback loop between theory and experiment for discovering this powerful psychological/societal dynamic. Much as early physical scientists sought unifying dynamics governing physical forces by rolling balls down slopes and experimenting on charged spheres, I see this as a "rolling balls down slopes" moment for discovering some key underlying dynamics by which our complex society evolves.