This article focuses on communication systems following Zipf’s law, in a study of the rel-ationship between the properties of those communication systems and the exponent of the law. The properties of communication systems are described using quantitative measures of semantic vagueness and the cost of word use. The precision and the economy of a communication system is reduced to a function of the exponent of Zipf’s law and the size of the communication system. Taking the exponent of the frequency spectrum, it is demonstrated that semantic precision grows with the exponent, where-as the cost of word use reaches a global minimum between 1.5 and 2, if the size of the communication system remains constant. The exponent of Zipf’s law is shown to be a key aspect for knowing about the number of stimuli handled by a communication system, and determining which of two systems is less vague or less expensive. The ideal exponent of Zipf’s law, it is therefore argued, should be very slightly above 2.Peer ReviewedPostprint (published version
