Zipf's Law: Balancing signal usage cost and communication efficiency

Christoph Salge; Nihat Ay; Daniel Polani; Mikhail Prokopenko

doi:10.1371/journal.pone.0139475

Zipf's Law: Balancing signal usage cost and communication efficiency

Christoph Salge, Nihat Ay, Daniel Polani, Mikhail Prokopenko

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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. Copyright:

Original language	English
Article number	e0139475
Journal	PLoS ONE
Volume	10
Issue number	10
DOIs	https://doi.org/10.1371/journal.pone.0139475
Publication status	Published - 1 Oct 2015

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10.1371/journal.pone.0139475Licence: CC BY

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Copyright: © 2015 Salge et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Final published version, 290 KBLicence: CC BY

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Zipf's Law: Balancing signal usage cost and communication efficiency

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