Generalized Galton’s boards explain social phenomena via statistical physics

Many aspects of our society are shaped by the repeated occurrence of small, random events. For instance, our personal wealth evolves based on how we spend and exchange money, while our opinions are constantly changing as a result of repeated interactions with both others and social media. This idea that the persistent repetition of random events can profoundly impact individuals was insightfully captured by Sir Francis Galton. He illustrated this concept using the device that now bears his name: Galton’s board. In this paper, we revisit the mathematical principles underlying Galton’s board and frame them within the broader context of statistical mechanics. We illustrate how the mechanisms behind the board can be generalized to model a wide range of social phenomena and to capture, in a new and simple way, the universal profile emerging from the details of the repeated elementary interactions.