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

Publikationstyp
Journal Article
Date Issued
2015-10-01
Sprache
English
Author(s)
Salge, Christoph  
Ay, Nihat 
Polani, Daniel  
Prokopenko, Mikhail  
Herausgeber*innen
Smalheiser, Neil R.  
TORE-URI
http://hdl.handle.net/11420/14224
Journal
PLOS ONE  
Volume
10
Issue
10
Article Number
e0139475
Citation
PLoS ONE 10 (10): e0139475 (2015-10-01)
Publisher DOI
10.1371/journal.pone.0139475
Scopus ID
2-s2.0-84947277949
PubMed ID
26427059
Publisher
PLOS
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.
DDC Class
510: Mathematik