Simon's fundamental rich-get-richer model entails a dominant first-mover advantage

TL;DR

This paper revises Herbert Simon's rich-get-richer model, revealing a dominant first-mover advantage that leads to overrepresentation of initial elements, challenging previous assumptions of a simple power-law distribution.

Contribution

The study demonstrates that Simon's model inherently favors the first element, providing a new analysis of long-term rankings and variability, and offers empirical evidence of the first-mover advantage.

Findings

First element size is disproportionately large due to first-mover advantage.

Expected time for a first replication is infinite, affecting long-term dynamics.

Empirical citation data supports the revised model with first-mover dominance.

Abstract

Herbert Simon's classic rich-get-richer model is one of the simplest empirically supported mechanisms capable of generating heavy-tail size distributions for complex systems. Simon argued analytically that a population of flavored elements growing by either adding a novel element or randomly replicating an existing one would afford a distribution of group sizes with a power-law tail. Here, we show that, in fact, Simon's model does not produce a simple power law size distribution as the initial element has a dominant first-mover advantage, and will be overrepresented by a factor proportional to the inverse of the innovation probability. The first group's size discrepancy cannot be explained away as a transient of the model, and may therefore be many orders of magnitude greater than expected. We demonstrate how Simon's analysis was correct but incomplete, and expand our alternate analysis to quantify the variability of long term rankings for all groups. We find that the expected time for a first replication is infinite, and show how an incipient group must break the mechanism to improve their odds of success. We present an example of citation counts for a specific field that demonstrates a first-mover advantage consistent with our revised view of the rich-get-richer mechanism. Our findings call for a reexamination of preceding work invoking Simon's model and provide an expanded understanding going forward.