title: Zipf's Law: Balancing Signal Usage Cost and Communication Efficiency.
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.
authors.affiliation: Department of Computer Science, University of Hertfordshire, Hatfield, United Kingdom.
authors.forename: Christoph
authors.initials: C
authors.lastname: Salge
authors.affiliation: Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany; Santa Fe Institute, Santa Fe, United States of America; Department of Mathematics and Computer Science, Leipzig University, Leipzig, Germany.
authors.forename: Nihat
authors.initials: N
authors.lastname: Ay
authors.affiliation: Department of Computer Science, University of Hertfordshire, Hatfield, United Kingdom; Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, Australia.
authors.forename: Daniel
authors.initials: D
authors.lastname: Polani
authors.affiliation: Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, Australia; Department of Computing, Macquarie University, Sydney, Australia.
authors.forename: Mikhail
authors.initials: M
authors.lastname: Prokopenko
mesh_terms: D003142:Communication; D006801:Humans; D007257:Information Theory; D007802:Language; D008962:Models, Theoretical; D013997:Time Factors