Emergence of Zipf's Law in the Evolution of Communication

TL;DR

This paper demonstrates that Zipf's law naturally emerges as the unique outcome of evolving communication systems when modeled through information-theoretic principles, specifically the tension between speaker and hearer efforts.

Contribution

It introduces a variational, information-theoretic framework showing Zipf's law as the inevitable result of communicative tension in evolving systems.

Findings

Zipf's law arises from the tension between speaker and hearer efforts.

The formalism is based on Kullback's Minimum Discrimination of Information Principle.

Zipf's law is the only expected outcome under the defined conditions.

Abstract

Zipf's law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and hearer in a communication system, we introduce evolution by means of a variational approach to the problem based on Kullback's Minimum Discrimination of Information Principle. Therefore, using a formalism fully embedded in the framework of information theory, we demonstrate that Zipf's law is the only expected outcome of an evolving, communicative system under a rigorous definition of the communicative tension described by Zipf.