The principle of least effort and Zipf distribution

"Each individual will adopt a course of action that will involve the expenditure of the probably least average of his work." This statement was named "the principle of least effort". The principle of least effort is often known as a "deterministic description of human behavior". In this paper, we present a brief introduction of this principle. Applications of the principle in different fields are also summarized. As the principle of least effort is proposed by Zipf, it is also called Zipf's law. We then discuss the correlation between three widely considered distributions: Zipf distribution, Pareto distribution and probability distribution. With empirical investigations, it is often stated that, most social behaviors are controlled by the pure Zipf's law that corresponds to the Zipf distribution of exponent -1. We summarily present the discovery of Zipf's law in different social behaviors. Some empirical studies are also given as examples, verifying that, in most countries, the distribution of city size by population follows Zipf's law, and the exponent of Zipf distribution of individual income is about -0.5, the same as Zipf predicted in theory.