Modeling Descriptive Norms in Multi-Agent Systems: An Auto-Aggregation PDE Framework with Adaptive Perception Kernels
Chao Li, Ilia Derevitskii, Sergey Kovalchuk
TL;DR
This work develops a PDE-based auto-aggregation framework for descriptive norms in autonomous multi-agent systems by coupling a nonlocal perception gradient with an external potential field, governing the evolution of a continuous opinion distribution $P(x,t)$ via $\partial_t P = d \nabla^2 P - \nabla \cdot [ P ( c G(P) - \nabla V(x) ) ]$, where $G(P)$ is defined through a kernel $g$ and a nonlocal interaction. The model is validated on a real COVID-19 clinical dataset, demonstrating that top-down guideline updates can drive convergence to new norms, bottom-up changes in medical facts via adaptive perception kernels can reconstruct norms aligned with observed practices, and fully autonomous interactions yield multicentric normative structures. A key methodological contribution is the use of continuous propensity fields derived from 33 binary medical features via Gaussian Mixture Models, linking discrete clinical decisions to the PDE dynamics and enabling robust statistical and causal analyses through methods like Mann-Whitney tests and Double Machine Learning. The framework provides a computable, data-driven tool for simulating descriptive norms, with practical implications for policy design, clinical pathway analysis, and autonomous agent governance, and it points to future extensions including higher-dimensional norm spaces and integration with prescriptive AI tools. Overall, the paper offers a principled bridge between nonlocal PDE-based opinion dynamics and real-world norm evolution in medical contexts, enabling interpretable exploration of how guidelines, medical realities, and autonomous interactions shape collective descriptive norms.
Abstract
This paper presents a PDE-based auto-aggregation model for simulating descriptive norm dynamics in autonomous multi-agent systems, capturing convergence and violation through non-local perception kernels and external potential fields. Extending classical transport equations, the framework represents opinion popularity as a continuous distribution, enabling direct interactions without Bayesian guessing of beliefs. Applied to a real-world COVID-19 dataset from a major medical center, the experimental results demonstrate that: when clinical guidelines serve as a top-down constraint mechanism, it effectively generates convergence of novel descriptive norms consistent with the dataset; in the bottom-up experiment, potential field guidance successfully promotes the system's reconstruction of descriptive norms aligned with the dataset through violation-and-recoupling; whereas fully autonomous interaction leads to the emergence of multi-centric normative structures independent of the dataset.