Preferential attachment. Definition[edit] A preferential attachment process is a stochastic urn process, meaning a process in which discrete units of wealth, usually called "balls", are added in a random or partly random fashion to a set of objects or containers, usually called "urns". A preferential attachment process is an urn process in which additional balls are added continuously to the system and are distributed among the urns as an increasing function of the number of balls the urns already have. In the most commonly studied examples, the number of urns also increases continuously, although this is not a necessary condition for preferential attachment and examples have been studied with constant or even decreasing numbers of urns. Linear preferential attachment processes in which the number of urns increases are known to produce a distribution of balls over the urns following the so-called Yule distribution.
For k ≥ k0 (and zero otherwise), where B(x, y) is the Euler beta function: History[edit] Power law. An example power-law graph, being used to demonstrate ranking of popularity. To the right is the long tail, and to the left are the few that dominate (also known as the 80–20 rule). In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another.
For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.[1] Empirical examples of power laws[edit] Properties of power laws[edit] Scale invariance[edit] One attribute of power laws is their scale invariance.
. , scaling the argument by a constant factor causes only a proportionate scaling of the function itself. That is, scaling by a constant simply multiplies the original power-law relation by the constant . And A power-law only if Universality[edit] Pareto principle. The Pareto Principle asserts that only a "vital few" peapods produce the majority of peas. The Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity)[1][2] states that, for many events, roughly 80% of the effects come from 20% of the causes.[3] Management consultant Joseph M.
Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who noted the 80/20 connection while at the University of Lausanne in 1896, as published in his first work, Cours d'économie politique. Essentially, Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. It is an axiom of business management that "80% of sales come from 20% of clients".[4] Richard Koch authored the book, The 80/20 Principle, which illustrated some practical applications of the Pareto principle in business management and life.[5] The Pareto principle is only tangentially related to Pareto efficiency.
In economics[edit] Jevons paradox. The Jevons paradox has been used to argue that energy conservation may be futile, as increased efficiency may increase fuel use. Nevertheless, increased efficiency can improve material living standards. Further, fuel use declines if increased efficiency is coupled with a green tax or other conservation policies that keep the cost of use the same (or higher).[3] As the Jevons paradox applies only to technological improvements that increase fuel efficiency, policies that impose conservation standards and increase costs do not display the paradox.
History[edit] The Jevons paradox was first described by the English economist William Stanley Jevons in his 1865 book The Coal Question. Jevons observed that England's consumption of coal soared after James Watt introduced his coal-fired steam engine, which greatly improved the efficiency of Thomas Newcomen's earlier design. Cause[edit] Rebound effect[edit] Khazzoom–Brookes postulate[edit] Energy conservation policy[edit] See also[edit] Peter Principle. An illustration visualizing the Peter principle The Peter Principle is a concept in management theory in which the selection of a candidate for a position is based on the candidate's performance in his or her current role rather than on abilities relevant to the intended role. Thus, employees only stop being promoted once they can no longer perform effectively, and "managers rise to the level of their incompetence. " The principle is named after Laurence J.
Peter who co-authored with Raymond Hull the humorous 1969 book The Peter Principle: Why Things Always Go Wrong. Overview[edit] The Peter Principle is a special case of a ubiquitous observation: Anything that works will be used in progressively more challenging applications until it fails. Peter suggests that "[i]n time, every post tends to be occupied by an employee who is incompetent to carry out its duties"[2] and that "work is accomplished by those employees who have not yet reached their level of incompetence. " Responses[edit]