Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2407.20451

Opinion response functions are key to understanding tipping of social conventions

Sarah K. Wyse·Eric Foxall
View original source ↗Read source document ↗Export metadata ↓

Abstract

The extent to which committed minorities can overturn social conventions is an active area of research in the mathematical modelling of opinion dynamics. Researchers generally use simulations of agent-based models (ABMs) to compute approximate values for the minimum committed minority size needed to overturn a social convention. In this manuscript, we expand on previous work by studying an ABM's mean-field behaviour using ordinary differential equation (ODE) models and a new tool, opinion response functions. Using these methods allows for formal analysis of the deterministic model which can provide a theoretical explanation for observed behaviours, e.g., coexistence or overturning of opinions. In particular, opinion response functions are a method of characterizing the equilibria in our social model. Our analysis confirms earlier numerical results and supplements them with a precise formula for computing the minimum committed minority size required to overturn a social convention.

Explore related subjects

physics.soc-phmath.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sarah K. Wyse, Eric Foxall. 2024-10-03. Opinion response functions are key to understanding tipping of social conventions. https://doi.org/10.1088/1742-5468%2Fad86b6

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-Reference in Large Language Models: The Introspection Threshold for Recursive Self-Improvement

The pursuit of self-evolving AI raises a critical question: when is autonomous self-improvement sustainable rather than degenerative? Drawing an analogy to von Neumann's complexity threshold for self-reproducing automata, we argue that sustainable recursive self-improvement in Large Language Models (LLMs) requires a functional analogue: introspection -- the system's capacity to simulate its own operations and target modifications. Grounded in Kleene's Second Recursion Theorem, we demonstrate the theoretical existence of such introspective programs. However, an empirical review reveals that while current LLMs exhibit quasi-introspection (e.g., partial metacognition), they fall short of true introspection due to structural bottlenecks: a lack of complete self-access, the feedforward nature of the Transformer, and computational class constraints that prevent fixed-point iteration. We conclude by outlining architectural paths to cross this complexity threshold and discussing the associated safety implications.

physics.soc-ph↗
arXiv2026

Multilayer Analysis of the Global Trade Network

Global trade is more than a single network of aggregate flows. Beneath the observable exchange of products among economies lies a complex multilayer structure, formed by thousands of product-specific trade relationships that differ in their similarity, interdependence, and temporal evolution. Using the CEPII's BACI database, which records bilateral product-level trade flows between economies, we represent the global trade network from 1995 to 2024 as a temporal multilayer network, with economies as nodes and directed weighted trade flows as edges. To investigate product-level organisation and cross-layer similarity, temporal structural change, and the structural role of individual economies, we introduce a random-walk-based similarity measure that provides a unified framework for comparing weighted and directed trade layers. Our results show that the global trade network remains relatively stable over short periods but undergoes gradual structural change over longer timescales. We also find that similarity-based product communities only partially align with the official product taxonomy, indicating that products assigned to the same official category do not necessarily exhibit similar trade-network structures. Finally, we show that an economy's structural influence is not always determined by its trade volume. These results highlight the value of multilayer network analysis for revealing patterns in global trade that remain hidden at the aggregate level.

physics.soc-ph↗
arXiv2026

Detectability limits of scaling laws

Power law scaling relations between size and output are central to quantitative theories of cities, organisms, and other complex systems. Competing theories predict scaling exponents that differ by small fractions, but there is no existing theory for verifying whether a given dataset can even distinguish exponents at the required resolution to address such discrepancies. Here we derive a resolution limit for scaling exponents, giving the smallest exponent difference that any method of analysis can detect. We find that the Hurst exponents governing the evolution of systems' sizes and deviations from the scaling law determine how long a record of growing systems must be before it can separate competing scaling theories. Empirical results suggest that many available data panels are insufficient for reliable scaling model selection.

physics.soc-ph↗