On Early Stages of Idea Propagation, the Number of Adopters Grows as n(t) ~ c * ta: Theoretical Explanation of the Empirical Observation

Authors

L. Octavio Lerma, The University of Texas at El PasoFollow
Deana Pennington, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-2013

Comments

Technical Report: UTEP-CS-13-52

To appear in Journal of Uncertain Systems, 2014, Vol. 8.

Abstract

New good ideas sometimes propagate too slowly. To speed up their propagation, we need to have a quantitative understanding of how ideas propagate. An intuitive understanding of ideas propagation has led to several reasonable first-approximation mathematical models. These models provide a good description of idea propagation on the later stages, when the ideas have already been adopted by a reasonably large number of people. However, at the critically important early stages, these models are not perfect: these models predict a linear growth with time, while empirical growth data is often better described by a power law. In this paper, we provide an intuitive theoretical explanation of the observed power-law growth.