Santa Fe Institute

SFI Working Paper Abstract

Title: Zipf’s Law: Balancing Signal Usage Cost and Communication Efficiency
Author(s): Christoph Salge, Nihat Ay, Daniel Polani, Mikhail Prokopenko
Files: [pdf]
Paper #: 13-10-033
Date: Oct. 31, 2013
Abstract: We propose a model that explains the reliable emergence of power laws (e.g., Zipf’s law) during the development of different human languages. The model incorporates the principle of least effort in communications, minimizing a combination of the information-theoretic communication inefficiency and direct signal cost. We prove a general relationship, for all optimal languages, between the signal cost distribution and the resulting distribution of signals. Zipf’s law then emerges for logarithmic signal cost distributions, which is the cost distribution expected for words constructed from letters or phonemes.

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