Convergence of knowledge in a cultural evolution model with population structure, random social learning and credibility biases

TL;DR

This paper introduces a mathematical model to study how knowledge spreads and converges in human populations, considering social learning, population structure, and credibility biases, with theoretical analysis and simulations.

Contribution

It presents a novel mathematically oriented model combining features of individual-based approaches and learning algorithms, with analysis and simulations to understand knowledge convergence.

Findings

Model exhibits convergence of knowledge under certain conditions

Theoretical properties are established for simplified cases

Numerical simulations illustrate model behavior

Abstract

Understanding how knowledge is created and propagates within groups is crucial to explain how human populations have evolved through time. Anthropologists have relied on different theoretical models to address this question. In this work, we introduce a mathematically oriented model that shares properties with individual based approaches, inhomogeneous Markov chains and learning algorithms, such as those introduced in [F. Cucker, S. Smale, Bull. Amer. Math. Soc., 39 (1), 2002] and [F. Cucker, S. Smale and D.~X Zhou, Found. Comput. Math., 2004]. After deriving the model, we study some of its mathematical properties, and establish theoretical and quantitative results in a simplified case. Finally, we run numerical simulations to illustrate some properties of the model.