{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/opinion-response-functions-are-key-to","title":"Opinion response functions are key to understanding tipping of social conventions","arxiv_id":"2407.20451","date":"2024-07-29","proceeding":null,"authors":["Sarah K. Wyse","Eric Foxall"],"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.","url_abs":"https://arxiv.org/abs/2407.20451v3","url_pdf":"https://arxiv.org/pdf/2407.20451v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"opinion-response-functions-are-key-to","repo_url":"https://github.com/sarahwyse/opinionresponsefunctions","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}