Faster is More Different: Mean-Field Dynamics of Innovation Diffusion

TL;DR

This paper models how faster innovation leads to a broader and more skewed distribution of ideas in society, challenging traditional views and aligning with empirical observations.

Contribution

It introduces a mean-field model of innovation diffusion showing that rapid progress results in diverse idea distributions and fewer innovators than previously assumed.

Findings

Faster innovation correlates with broader idea distribution.

Innovative societies have fewer innovators than traditional theories suggest.

Distribution of ideas is skewed with slow adoption saturation.

Abstract

Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a highly innovative society is not characterized by heavy concentration in highly valued ideas: Rather, ideas are more broadly distributed in a more innovative society with faster progress, provided that the rate of adoption is constant, which suggests a positive correlation between innovation and technological disparity. Furthermore, the distribution is generally skewed in such a way that the fraction of innovators is substantially smaller than has been believed in conventional innovation-diffusion theory based on normality. Thus, the typical adoption pattern is predicted to be asymmetric with slow saturation in the ideal situation, which is compared with empirical data sets.