In sociology, the Matthew effect (or accumulated advantage) is the phenomenon where "the rich get richer and the poor get poorer." In both its original and typical usage it is meant metaphorically to refer to issues of fame or status but it may also be used literally to refer to cumulative advantage of economic capital. The term was first coined by sociologist Robert K. Merton in 1968 and takes its name from a verse in the biblical Gospel of Matthew, pertaining to Jesus' parable of the talents:
For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken even that which he hath.
In network science, the Matthew effect is used to describe the preferential attachment of earlier nodes in a network, which explains that these nodes tend to attract more links early on.  "Because of preferential attachment, a node that acquires more connections than another one will increase its connectivity at a higher rate, and thus an initial difference in the connectivity between two nodes will increase further as the network grows, while the degree of individual nodes will grow proportional with the square root of time."  The Matthew Effect therefore explains the growth of some nodes in vast networks such as the Internet. 
Sociology of science
In the sociology of science, "Matthew effect" was a term coined by Robert K. Merton to describe how, among other things, eminent scientists will often get more credit than a comparatively unknown researcher, even if their work is similar; it also means that credit will usually be given to researchers who are already famous. For example, a prize will almost always be awarded to the most senior researcher involved in a project, even if all the work was done by a graduate student. This was later formulated by Stephen Stigler as Stigler's law — "No scientific discovery is named after its original discoverer" — with Stigler explicitly naming Merton as the true discoverer, making his "law" an example of itself.
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As credit is valued in science, specific claims of the Matthew effect are contentious. Many examples below exemplify more famous scientists getting credit for discoveries due to their fame, even as other less notable scientists had preempted their work.
- Laboratory and natural experiments manipulate download counts or bestseller lists for books and music show consumer activity follows the apparent popularity.
- In algorithmic information theory, the notion of Kolmogorov complexity is named after the famous mathematician Andrey Kolmogorov even though it was independently discovered and published by Ray Solomonoff a year before Kolmogorov. Li and Vitanyi, in "An Introduction to Kolmogorov Complexity and Its Applications" (p. 84), write:
- Ray Solomonoff [...] introduced [what is now known as] "Kolmogorov complexity" in a long journal paper in 1964. [...] This makes Solomonoff the first inventor and raises the question whether we should talk about Solomonoff complexity. [...]
- There are many uncontroversial examples of the Matthew effect in mathematics, where a concept is due to one mathematician (and well-documented as such), but is attributed to a later (possibly much later), more famous mathematician who worked on it. For instance, the Poincaré disk model and Poincaré half-plane model of hyperbolic space are both named for Henri Poincaré, but were introduced by Eugenio Beltrami in 1868 (when Poincaré was 14 and had not as yet contributed to hyperbolic geometry).
- A model for career progress quantitatively incorporates the Matthew Effect in order to predict the distribution of individual career length in competitive professions. The model predictions are validated by analyzing the empirical distributions of career length for careers in science and professional sports (e.g. Major League Baseball). As a result, the disparity between the large number of short careers and the relatively small number of extremely long careers can be explained by the "rich-get-richer" mechanism, which in this framework, provides more experienced and more reputable individuals with a competitive advantage in obtaining new career opportunities.
- In his 2011 book The Better Angels of Our Nature: Why Violence Has Declined, cognitive psychologist Steven Pinker refers to the Matthew Effect in societies, whereby everything seems to go right in some, and wrong in others. He speculates in Chapter 9 that this could be the result of a positive feedback loop in which reckless behavior by some individuals creates a chaotic environment that encourages reckless behavior by others. He cites research by Martin Daly and Margo Wilson showing that the more unstable the environment, the more steeply people discount the future, and thus the less forward-looking their behavior.
In science, dramatic differences in the productivity may be explained by three phenomena: sacred spark, cumulative advantage, and search costs minimization by journal editors. The sacred spark paradigm suggests that scientists differ in their initial abilities, talent, skills, persistence, work habits, etc. that provide particular individuals with an early advantage. These factors have a multiplicative effect which helps these scholars succeed later. The cumulative advantage model argues that an initial success helps a researcher gain access to resources (e.g., teaching release, best graduate students, funding, facilities, etc.), which in turn results in further success. Search costs minimization by journal editors takes place when editors try to save time and effort by consciously or subconsciously selecting articles from well-known scholars. Whereas the exact mechanism underlying these phenomena is yet unknown, it is documented that a minority of all academics produce the most research output and attract the most citations.
In education, the term "Matthew effect" has been adopted by psychologist Keith Stanovich to describe a phenomenon observed in research on how new readers acquire the skills to read: early success in acquiring reading skills usually leads to later successes in reading as the learner grows, while failing to learn to read before the third or fourth year of schooling may be indicative of lifelong problems in learning new skills. This is because children who fall behind in reading would read less, increasing the gap between them and their peers. Later, when students need to "read to learn" (where before they were learning to read), their reading difficulty creates difficulty in most other subjects. In this way they fall further and further behind in school, dropping out at a much higher rate than their peers.
In the words of Stanovich:
Slow reading acquisition has cognitive, behavioral, and motivational consequences that slow the development of other cognitive skills and inhibit performance on many academic tasks. In short, as reading develops, other cognitive processes linked to it track the level of reading skill. Knowledge bases that are in reciprocal relationships with reading are also inhibited from further development. The longer this developmental sequence is allowed to continue, the more generalized the deficits will become, seeping into more and more areas of cognition and behavior. Or to put it more simply – and sadly – in the words of a tearful nine-year-old, already falling frustratingly behind his peers in reading progress, "Reading affects everything you do."
- Matilda effect
- Capital accumulation
- The internal contradictions of capital accumulation
- Preferential attachment
- Positive feedback
- Virtuous circle and vicious circle
- Wealth condensation
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