Do Those Who Have Receive More? Mechanisms, Causal Identification, and Limits of Cumulative Advantage and the Matthew Effect in the Academic Literature

Does an initial advantage produce further advantages?

The Gospel according to Matthew contains a passage stating that those who have will be given more, and that those who have not will lose even what they have. Merton (1968) used this passage to name the Matthew effect, a bias in the reward system of science. In interviews, Nobel laureates repeatedly observed that eminent scientists receive disproportionately great credit for their contributions, whereas relatively unknown scientists receive disproportionately little credit for comparable contributions. The process by which those who were initially advantaged keep accumulating advantages is called cumulative advantage. The abstract of DiPrete and Eirich (2006) describes cumulative advantage as a concept originally developed by Merton to explain scientific careers and later generalized into a mechanism of inequality for temporal processes such as the life course and family generations.

This idea can be read in two ways. In the first reading, people who keep winning were better from the start, and the difference was gradually revealed over time. In the second reading, a small and sometimes arbitrary initial advantage attracts later opportunities and recognition, and these enlarge the difference. van de Rijt et al. (2014) set these two explanations side by side and noted that, in observational data, the two are confounded and difficult to separate. This is because the correlation in which past winners win again can arise both from unobserved differences in ability and from a process in which success breeds success.

If the two cannot be separated, the everyday statement that “the gap only keeps widening” has not yet been tested either. This note reads the literature on cumulative advantage by separating three questions: what produces what (mechanism), how this was tested (identification), and how large the effect is and where it stops (magnitude and limits). The answer reached at the end is that cumulative advantage exists as a force that widens gaps, but the evidence does not support the claim that gaps necessarily widen.

Scope and method

• Target: peer-reviewed papers on cumulative advantage, cumulative disadvantage, the Matthew effect, success-breeds-success processes, and preferential attachment. The sources were collected under six topics: concept and lineage, life course and health, causal identification (experiments and quasi-experiments), education and development, network mechanisms, and counterevidence and limits.
• Collection: candidates were collected across academic databases (OpenAlex, Crossref, Semantic Scholar, PMC, and NBER), and 36 sources remained after duplicates, retracted papers, and predatory journals were removed. Books (Rigney 2010, and Frank and Cook on winner-take-all markets) were excluded because their full texts could not be checked. Simon (1955) and Cobley et al. (2009) were excluded because neither the full text nor the abstract could be obtained.
• Verification: for 29 of the 36 sources, the full text was obtained, and the numbers and claims were checked against the relevant passages. Some sources were read in working paper versions (Azoulay et al., Simcoe and Waguespack, Cunha and Heckman, Black et al., and Borjas and Doran). For these sources, only claims consistent with the abstract of the published version were used. For the 7 sources whose full texts could not be obtained (Allison et al. 1982, DiPrete and Eirich 2006, Dannefer 2003, O’Rand 1996, Ross and Wu 1996, Bedard and Dhuey 2006, and Rossiter 1993), claims were attributed to the authors within the range stated in the abstracts.
• Presentation: for each study, the mechanism, the identification strategy, and the magnitude and limits of the effect are described separately.

What did the Matthew effect and cumulative advantage originally refer to?

The Matthew effect in Merton (1968) was originally a narrow concept. It referred to the accruing of greater increments of recognition for particular scientific contributions to scientists of considerable repute and the withholding of such recognition from scientists who have not yet made their mark. The evidence was the testimony of Nobel laureates, which Merton called “presumptive evidence.” The reasoning was that the laureates testified not as victims but as unwitting beneficiaries, so there was little reason to discount their testimony.

Merton (1968) evaluated this bias from two sides. For the careers of individual scientists whose recognition is reduced at early stages, the Matthew effect is dysfunctional. For the communication system of science, however, new findings attached to eminent names become more visible, and the effect therefore helps findings spread. Citing a study by Cole and Cole, Merton reported that the visibility scores of physicists were 85 for Nobel laureates, 72 for members of the National Academy of Sciences, 38 for recipients of less prestigious awards, and 17 for physicists without awards.

In a later part of the same paper, Merton (1968) turned from recognition to the allocation of research resources. Centers of demonstrated excellence receive far larger resources, and their prestige attracts a disproportionate share of promising graduate students. Merton described this as the principle of cumulative advantage, in which “the rich get richer at a rate that makes the poor become relatively poorer.” Therefore, at the starting point, the bias in recognition (the Matthew effect) and the concentration of resources (cumulative advantage) were described as related but distinct phenomena.

Twenty years later, Merton (1988) redefined cumulative advantage. In this definition, initial comparative advantages of trained capacity, structural location, and available resources produce successive increments of advantage, and the gaps between the haves and the have-nots widen “until dampened by countervailing processes.” Merton himself, therefore, did not claim that gaps widen without limit. However, he also wrote that such countervailing processes had not yet been systematically investigated, and he only speculated about them, for example about an excessive concentration of talent in one place.

Subsequent work developed in two directions: modeling the process mathematically and clarifying the concept. Price (1976) proposed the cumulative advantage distribution, which represents situations in which success breeds success as a stochastic process. In this model, the probability of success increases with past success, whereas a lack of success does not increase the chance of failure. Price showed that this model, with a single free parameter, reproduces skewed distributions such as citation frequencies and Lotka’s law.

On the conceptual side, the abstract of DiPrete and Eirich (2006) states that the term cumulative advantage has developed multiple meanings in sociology, and the review distinguishes these meanings. The abstract defines cumulative advantage as a general process in which a favorable relative position becomes a resource that produces further relative gains. Bask and Bask (2015) went further and distinguished cumulative (dis)advantage, an intra-individual phenomenon in which advantages or disadvantages accumulate within a person, from the Matthew effect, an inter-individual phenomenon in which differences between people widen. They argued that the Matthew effect should be measured as a property of the process that generates inequality rather than as the size of the gap, and that “Matthew mechanism” is a better name.

Separating the process, the divergence between individuals, and the shape of the distribution

Extending the distinction of Bask and Bask (2015), claims about cumulative advantage have at least three levels. The first is a claim about the process: success at one point increases the probability of later success. The second is a claim about divergence between individuals: differences between people (variance or inequality indices) grow over time. The third is a claim about the shape of the distribution: outcomes become concentrated in a few people, producing a heavy-tailed distribution.

These three claims do not imply one another. According to the abstract of Allison, Long, and Krauze (1982), a mathematical model of cumulative advantage does not by itself imply increasing inequality. Increasing inequality is implied only when the model is modified to allow for heterogeneity in the rate of cumulative advantage. When they followed true cohorts of chemists and biochemists, inequality increased for publication counts but not for counts of citations to all previous publications (abstract).

A heavy-tailed distribution is also not evidence of cumulative advantage. van de Rijt et al. (2014) noted that some studies have treated the extreme variance of success distributions as a sign of cumulative advantage, whereas critics have pointed out that other mechanisms, such as a convex correspondence between ability and success, can generate the same regularities. Unobserved differences in ability also create an apparent bias toward past winners. Separating the three levels makes it possible to see which level each of the following studies tested.

What happens when early success is assigned at random?

A direct way to test the process level is to assign early success at random and compare what follows. Random assignment makes the ability of recipients and nonrecipients equal on average, so later differences can be attributed to the assigned success itself.

van de Rijt et al. (2014) conducted such experiments on four real websites. They randomly assigned donations on the crowdfunding site Kickstarter, “very helpful” ratings on the review site Epinions, awards to editors on Wikipedia, and signatures on the petition site Change.org. In all four settings, the recipients of early success experienced significantly more subsequent success than nonrecipients. In the funding study, the average number of subsequent donations from third parties increased from 1.11 in the control condition to 2.49 in the experimental condition.

However, the same experiments also measured how far the gap widened. In the funding study, the condition with one donation and the condition with four donations did not differ significantly in the chance of receiving further donations (χ² = 1.65, P = .199). In the endorsement study, 77% of good reviews that received no rating from the researchers, 90% of those that received one rating, and 94% of those that received four ratings later received ratings from others, and the one-rating and four-rating conditions did not differ significantly. An increase from zero to one had an effect, but additional increases from one to four had little effect. The authors called this decreasing marginal returns and concluded that reward systems are less vulnerable to incidental or fabricated advantages than previously thought, and that cumulative advantage plays a more modest role in explaining social inequality.

The Wikipedia part of this experiment had a predecessor. Restivo and van de Rijt (2012) took 200 editors who were among the 1% most productive and had never received an award (barnstar), randomly divided them into two groups, and gave awards to 100 of them. After 90 days, the median productivity of the award group was 60% higher than that of the control group. Twelve editors in the award group and two in the control group subsequently received awards from other editors. The 12 editors who received further awards had not been more productive than others in the same group before receiving them, so the authors interpreted the accumulation of awards as operating through enhanced social prestige in the community rather than through increased merit. In this study, two pathways were observed at the same time: recognition that elicits individual effort, and recognition that attracts further recognition.

Salganik, Dodds, and Watts (2006) showed how a success-breeds-success process affects overall inequality. They asked 14,341 participants to listen to and download songs by unknown bands, and randomly assigned participants to an “independent” condition, in which the download counts of others were not shown, or to a “social influence” condition, in which they were shown. The social influence condition was divided into eight independent “worlds,” in each of which popularity developed separately. In all eight worlds, the inequality of success (Gini coefficient) was greater than in the independent condition, and which songs succeeded also differed between worlds. The quality of a song (its popularity in the independent condition) only partly determined its success: the best songs rarely did poorly and the worst rarely did well, but any other result was possible. This experiment shows that information about the choices of others increases both inequality and unpredictability.

Bol, de Vaan, and van de Rijt (2018) asked the same question within a real institution. In a Dutch funding program for early career researchers, all applicants above a review score threshold received funding, and all applicants below it did not. Applicants just above and just below the threshold had nearly identical review scores, so the funding decision could be treated as a quasi-experiment (regression discontinuity). Winners just above the threshold received more than twice as much research funding over the following 8 years as nonwinners just below it (a difference of about 180,000 euros). This gap accounts for 40% of the difference in funding between the best and worst applicants (450,000 euros).

Bol et al. (2018) also examined where the gap came from. They found no evidence that winners succeeded in later competitions because of achievements enabled by the first grant. Instead, a substantial portion of the increase in the probability of winning a midcareer grant from 10% to 26% was accounted for by an increase in application rates from 40% to 59%. The difference in applications was caused not by nonwinners leaving academia or moving abroad, but by their decisions not to take part in later competitions. The authors called this a “participation” mechanism. Early failure creates gaps not only through the evaluations of others but also through the decision of the person concerned to withdraw from later competition.

Status matters when quality is difficult to observe

If early success produces later success, is this because evaluators use status as a substitute for quality? This question is difficult to answer unless status can be changed while quality is held constant.

Azoulay, Stuart, and Wang (2014) used appointment as a Howard Hughes Medical Institute (HHMI) Investigator as a change in status and examined whether citations to articles published before the appointment increased after it. Because the articles had already been published, the appointment could not change their quality. As controls, they precisely matched each article with articles by early career prize winners whose records before the appointment were similar. Citations increased after the appointment, but the effect was small and limited to a short window of time. However, the effect was significantly larger when there was uncertainty about article quality (for example, articles in low-impact journals or in novel areas) and when the prize winners had relatively low status at the time of appointment. The authors wrote that existing estimates may overstate the effect of status, and they titled their paper “Matthew: Effect or Fable?”

Simcoe and Waguespack (2011) used a natural experiment at the Internet Engineering Task Force (IETF), a standards organization for internet technologies. In e-mails announcing new submissions, author names were sometimes replaced with “et al.” when submission volumes were unusually high. By comparing the effect of obscuring high-status versus low-status author names, they found that name-based signals could explain up to three-quarters of the difference in publication rates between high-status and low-status authors. However, this effect disappeared for prescreened proposals that received more scrutiny than a typical submission. The authors interpreted this as indicating that status signals are more important when attention is scarce (or search costs are high).

The two studies point in the same direction. Status effects exist, but they become smaller when evaluators can directly check quality and larger when quality is difficult to observe or attention is scarce. The strength of cumulative advantage depends on how well quality can be observed in the evaluation setting.

Are those who lose early always left behind?

In the story of cumulative advantage, those who lose early accumulate disadvantages. However, some studies show that some people improve after an early setback.

Wang, Jones, and Wang (2019) compared junior scientists who applied for the main research grant (R01) of the US National Institutes of Health (NIH): 623 applicants whose scores fell just below the funding threshold (near misses) and 561 applicants whose scores fell just above it (narrow wins). A near miss increased attrition: in the regression discontinuity estimate, it led to a 12.6% chance of disappearing permanently from the NIH system over the next 10 years. Meanwhile, among the papers published by the near-miss group in the following 5 years, 16.1% were in the top 5% of citations for the same year and field, compared with 13.3% for the narrow-win group. In the regression discontinuity estimate, one early near miss increased the probability of publishing a top 5% paper in the next 10 years by 6.1%. The near-miss group received 0.29 million dollars less NIH funding per person in the first 5 years, but the funding difference disappeared in the second 5 years.

This result might appear to be explained by screening, in which weaker people left and only stronger people remained. Wang et al. (2019) removed the narrow winners who had published the fewest top 5% papers until the attrition rates of the two groups were equal, and the near-miss advantage remained; they concluded that screening alone could not fully explain the difference. An early setback accumulates disadvantage by increasing attrition, but it works in the opposite direction by improving the performance of those who remain.

Evidence in the opposite direction also exists for prizes. Borjas and Doran (2015) compared winners of the Fields Medal in mathematics with similarly brilliant contenders. The two groups had similar publication rates until the award year, after which the productivity of the winners declined. The medalists began to study unfamiliar topics at the expense of writing papers. A prize increases the resources and recognition of the winner, but it also changes how later effort is allocated.

The effect of research funding itself may also be smaller than commonly assumed. Using all applications to NIH R01 grants from 1980 to 2000, Jacob and Lefgren (2011) estimated that receiving a grant (worth roughly 1.7 million dollars) leads to only one additional publication over the next 5 years, a 7% increase. The authors interpreted this as consistent with a competitive market for research funding in which researchers who lose an NIH grant shift to another source of funding. An initial difference in resources does not necessarily accumulate directly into a difference in output.

Do gaps widen in school?

In education, the term Matthew effect was popularized by Stanovich (1986). As a framework for explaining the development of individual differences in reading, Stanovich proposed reciprocal causation between reading ability and reading volume. Children who read well read more, reading more increases vocabulary and knowledge, and these in turn make further reading easier. Stanovich cited an observation that some skilled first-grade groups read three times as many words a week as some less skilled groups (Allington 1984). He argued that the large differences in reading volume, combined with the importance of the existing knowledge base, could mean that a “rich-get-richer” cumulative advantage phenomenon is almost inextricably embedded in reading development.

When tested, this framework received only weak support. Pfost et al. (2014) systematically reviewed 25 years of empirical research on Matthew effects in reading development. Neither a pattern of widening gaps nor a pattern of narrowing gaps received general strong support. In a meta-analysis of studies reporting correlations between initial level and growth, the mean correlation was small and negative (r = −.214), meaning that children with higher initial levels tended to grow slightly less. Widening patterns were more likely for measures of decoding efficiency, vocabulary, and composite reading scores when the tests did not have problems with measurement precision.

Cunha and Heckman (2007) described skill formation in the language of economics. They defined self-productivity as the case in which skills in one period raise skills in the next period, and dynamic complementarity as the case in which skills acquired by one period make investment in that period more productive. Together, the two produce multiplier effects through which skills beget skills. In this model, there is no trade-off between equity and efficiency for early investments, but there is one for late investments. The claim that early interventions to reduce gaps are also efficient is therefore a prescription that presupposes a cumulative advantage process.

School institutions can also fix gaps in place. Harden et al. (2020) showed that mathematics course placement in the 9th grade in US high schools strongly determines later mathematics attainment. Of students enrolled in geometry or higher in the 9th grade, 44% ultimately completed calculus, compared with 4.2% of those in Algebra 1 and 1% of those in lower-level classes. Knigge et al. (2022) showed, using Dutch twins, that when tracking was delayed, the contribution of the shared environment to educational attainment fell from 27% to 2%. Early tracking is a point at which differences between families are translated into educational paths.

On whether teacher expectations accumulate gaps, a review reached a negative conclusion. Based on 35 years of research, Jussim and Harber (2005) concluded that self-fulfilling prophecies in the classroom do occur, but that their effects are typically small, do not accumulate greatly across perceivers or over time, and may be more likely to dissipate than accumulate. However, they also noted that powerful self-fulfilling prophecies may selectively occur among students from stigmatized social groups.

How long does the advantage of being born early last?

School cutoff dates create an age difference of almost one year within the same grade, regardless of ability. How far this difference persists into later outcomes provides a natural experiment on whether arbitrary initial advantages accumulate.

In sports, this relative age effect appears clearly. Musch and Grondin (2001) reviewed the phenomenon in which the birth dates of participants in age-grouped youth sport and in professional leagues are skewed toward the months just after the cutoff date. Children born shortly before the cutoff date are the youngest in their group and face unequal competition. The relative age effect is found in many competitive sports worldwide, but not in all of them, and both physical and psychological mechanisms have been proposed.

In academic outcomes, the gap persists but becomes smaller. According to the abstract of Bedard and Dhuey (2006), across OECD countries, the youngest members of each cohort scored 4 to 12 percentiles lower than the oldest members in grade 4 and 2 to 9 percentiles lower in grade 8. Data from Canada and the United States showed that the youngest members were also less likely to attend university. Campbell (2014) showed, using 5,481 seven-year-olds in England, that birth-month differences in teachers’ judgments of ability were larger when pupils were grouped by ability within the class. The grouping arrangement converts an arbitrary difference in age into a difference in perceived ability.

However, over longer periods, the gap disappears in some domains. Using data on the population of Norway, Black, Devereux, and Salvanes (2011) separated the effect of school starting age from the effect of age at test. For IQ measured at military enrollment around age 18, there was no advantage of starting school older; instead, starting school younger had a small positive effect, and age at test had a much larger effect. School starting age had little effect on educational attainment, and the short-run positive effect on earnings of starting school younger had essentially disappeared by age 30. Arbitrary initial differences can persist or disappear depending on the domain and the time at which they are measured.

Do health gaps widen over the life course?

Gerontology adopted cumulative advantage and cumulative disadvantage as the question of whether differences within the same cohort widen with age. Ferraro and Shippee (2009) cite the definition by Dannefer (2003) of this process as the “systematic tendency for interindividual divergence in a given characteristic (e.g., money, health, status) with the passage of time.” The abstract of O’Rand (1996) states that institutions such as labor markets and pensions stratify the availability of resources and rewards and interact with life-course processes such as labor force history and job mobility to produce complex patterns of cumulative advantage and cumulative disadvantage.

Empirical results include both widening and nonwidening gaps. According to the abstract of Ross and Wu (1996), in two US national samples (cross-sectional data on 2,031 respondents and two-wave data on 2,436 respondents), the gaps in self-reported health, physical functioning, and physical well-being between people with high and low educational attainment were larger at older ages. Leopold and Engelhardt (2013), using two waves of data on 14,818 Europeans aged 50 to 80, found that educational inequality increased significantly in limitations of physical functioning and grip strength, whereas the gap remained constant in chronic diseases and self-rated health. Whether the gap widened depended on which dimension of health was measured.

Ferraro and Shippee (2009) summarized the theory in this area as cumulative inequality theory with five axioms. The second axiom states that disadvantage increases exposure to risk, whereas advantage increases exposure to opportunity, and the authors asked that disadvantage not be treated as the inverse of advantage. The third axiom states that life course trajectories are shaped by the accumulation of risk, available resources, and human agency, and the authors stated explicitly that early disadvantage does not determine a life. The fifth axiom states that if cumulative inequality leads to premature mortality, nonrandom selection may give the appearance of decreasing inequality in later life.

Is a heavy-tailed distribution evidence of cumulative advantage?

In network science, cumulative advantage was formalized as preferential attachment. Barabási and Albert (1999) showed that two mechanisms, the continuous addition of new vertices and the preferential attachment of new vertices to already well-connected vertices, produce a power-law distribution of connections. When either of the two ingredients was missing, the stationary power-law distribution observed in real networks did not appear. In the network of movie actors who appeared in the same films, the tail of the distribution of connections followed a power law with an exponent of 2.3.

Petersen et al. (2011) quantified the Matthew effect using career length. They built a stochastic model in which progress becomes easier as a person advances in a career and fitted it to the distributions of career length for 400,000 scientists who published in six journals and more than 20,000 athletes in four professional leagues. The model reproduced a distribution with many very short careers and some very long ones, and showed that many careers are stunted by the relative disadvantage associated with inexperience. However, the authors themselves wrote that the progress rate in the model combines talent, reputation, and productivity, and that more detailed data would be required to determine the role of each factor.

Pluchino et al. (2018) used a simple agent-based model in which talent is normally distributed and lucky and unlucky events occur at random, and showed that the most successful individuals are often not the most talented but people of average talent who are considerably luckier. This is a model showing that, if a cumulative process exists, chance can turn into large differences; it is not evidence that real success is determined by luck.

The three studies show that a cumulative advantage process can produce heavy-tailed distributions. However, as noted above, heavy-tailed distributions can also arise from other processes. Because the process cannot be inferred from the shape of the distribution, its existence can only be tested by experiments and quasi-experiments that manipulate early success.

When gaps appear to widen and when they do not

Even if the process exists, it is not necessarily observed as a widening of differences between individuals. At least four factors affect this observation.

The first is differences in accumulation rates between individuals. According to the abstract of Allison et al. (1982), a cumulative advantage model implies increasing inequality only when the rate of accumulation is assumed to differ between people. If success simply breeds success at the same rate, gaps do not necessarily widen.

The second is measurement. Pfost et al. (2014) classified tests with floor or ceiling effects, or with reliability below .85, as tests with low measurement precision. Widening patterns were more likely for tests without problems of measurement precision. When measurement is coarse, the widening of gaps can disappear from the observations.

The third is selective attrition. As the fifth axiom of Ferraro and Shippee (2009) states, if people with greater disadvantages die earlier, differences among the remaining older adults appear smaller. The attrition of near misses in Wang et al. (2019) also shows that comparing only those who remain makes the disadvantage of an early setback harder to see. The appearance of narrowing gaps does not mean that cumulative disadvantage was absent.

The fourth is that cumulative advantage can be counted as a genetic contribution. Using 11,000 pairs of twins from four countries, Haworth et al. (2010) showed that the heritability of general cognitive ability increases linearly from 41% at age 9 to 55% at age 12 and 66% at age 17. As a candidate explanation, they proposed a genotype-environment correlation in which children increasingly select, modify, and create their own experiences in line with their genetic propensities as they grow up. Dickens and Flynn (2001) proposed a model with strong reciprocal causation between IQ and environment, and argued that this reciprocal causation produces a genotype-environment correlation that masks the potency of environmental effects. The model also explains why heritability increases with age. A cumulative process in which ability attracts environments and those environments raise ability can be counted as a genetic effect rather than an environmental effect in the decomposition used in twin studies.

Finally, who receives an initial advantage is not determined by chance alone. The abstract of Rossiter (1993) treats the many cases of women scientists who have been ignored, denied credit, or dropped from sight as a systematic bias corresponding to the second half of the same passage in Matthew (from those who have not, even what they have will be taken away), and names it the Matilda effect. Together with the observation by Jussim and Harber (2005) that powerful self-fulfilling prophecies may occur among stigmatized groups, this indicates that the starting points of accumulation can be created by biases in evaluation based on group membership.

What can be said about cumulative advantage?

Returning to the opening question, the process in which an initial advantage produces further advantages has been repeatedly confirmed by randomized experiments and quasi-experiments. In donations, ratings, awards, and signatures (van de Rijt et al. 2014), Wikipedia awards (Restivo and van de Rijt 2012), a music market (Salganik et al. 2006), and research funding (Bol et al. 2018), early success increased later success. The mechanism is not single, and the following pathways have been confirmed in separate studies.

• Evaluators use status as a substitute for quality (Azoulay et al. 2014; Simcoe and Waguespack 2011).
• Recognition elicits individual effort (Restivo and van de Rijt 2012).
• Those who lose withdraw from later competition (Bol et al. 2018).
• The choices of others attract attention (Salganik et al. 2006).

The pathway in which skills make later learning more effective (Stanovich 1986; Cunha and Heckman 2007) is plausible as theory, but in reading it has not received general support as a source of widening gaps (Pfost et al. 2014).

However, the claim that gaps necessarily widen is not supported. Increasing the initial advantage produced little further differentiation (van de Rijt et al. 2014). Status effects were small where quality could be observed (Azoulay et al. 2014; Simcoe and Waguespack 2011). Some people improved after an early setback (Wang et al. 2019), a prize sometimes reduced productivity (Borjas and Doran 2015), and differences in funding sometimes translated into only small differences in output (Jacob and Lefgren 2011). In reading ability (Pfost et al. 2014), school starting age and earnings (Black et al. 2011), and chronic diseases and self-rated health (Leopold and Engelhardt 2013), gaps did not widen. As Merton (1988) wrote, gaps widen until they are dampened by countervailing processes, and where they are dampened differs between settings.

Based on this review, this note proposes the following interpretation. The evidence for cumulative advantage mainly supports the process level. Whether the process appears as a widening of differences between individuals depends not only on the strength of the process but also on four factors: differences in accumulation rates between people, measurement precision, selective attrition, and countervailing processes. The heaviness of the tail of a distribution is not evidence of the process.

This interpretation would need revision if the following observations accumulated: results from multiple settings showing that later gaps keep widening in proportion to the size of a randomly assigned initial advantage. In that case, decreasing marginal returns would be only a property of particular settings, and cumulative advantage would need to be rewritten as a force that keeps widening gaps.

Gaps

• Empirical study of countervailing processes: the countervailing processes that Merton (1988) described as uninvestigated (excessive concentration of talent, substitution in a competitive funding market, and improvement after a near miss) have been observed individually by Jacob and Lefgren (2011) and Wang et al. (2019), but this collection found no study that compares, within one framework, the conditions under which gaps stop widening.
• Simultaneous measurement of intra-individual accumulation and inter-individual divergence: few empirical studies have measured, following the distinction of Bask and Bask (2015), both the accumulation within the same people and the widening of gaps in the group.
• Size and persistence of initial advantages: the observation periods of randomized experiments are short (14 days for ratings on Epinions and 90 days in Restivo and van de Rijt 2012), so evidence on how many years an initial advantage persists depends on regression discontinuity studies (8 years in Bol et al. 2018 and 10 years in Wang et al. 2019).
• Linking evaluation bias and accumulation: within the scope of this note, no study that causally identifies how much biases based on group membership, such as the Matilda effect, create the starting points of cumulative advantage could be checked in its full text (only the abstract of Rossiter 1993 was available).
• Related notes: the problem of cumulative advantage concentrating both opportunities and burdens on highly capable people is discussed in Why Is the Stress of Outperformers Hard to Voice? Evidence on Displaying Competence, Being Envied, Hiding Success, and Invisible Effort, and the heritability of traits related to effort, together with the possibility that heritability includes environmental effects, is discussed in Is the Ability to Make an Effort Also a Talent? The Heritability of Grit, Self-Control, and Motivation to Learn, and How Far These Traits Can Be Changed.
• The first advantage and luck: whether the initial advantage from which accumulation starts is luck, and if so what kind of luck (option luck and brute luck, initial and later luck, ex ante and ex post), is discussed in Is the First Advantage Luck? Option Luck and Brute Luck, Ex Ante and Ex Post, and the Evidence on Initial Advantages and Fairness Judgments in the Academic Literature.

Unverified items

• No major claim remains unverified.
• Seven sources whose full texts could not be obtained were treated within the range of their abstracts (Allison et al. 1982, DiPrete and Eirich 2006, Dannefer 2003, O’Rand 1996, Ross and Wu 1996, Bedard and Dhuey 2006, and Rossiter 1993). In the text, all of them are attributed to the authors with “according to the abstract.”
• The definition by Dannefer (2003) was checked through the quotation in the full text of Ferraro and Shippee (2009).

References

All URLs were accessed on 2026-10-09.

Concept and lineage

• Merton, R. K. (1968). The Matthew effect in science. Science, 159(3810), 56–63. https://doi.org/10.1126/science.159.3810.56
• Merton, R. K. (1988). The Matthew effect in science, II: Cumulative advantage and the symbolism of intellectual property. Isis, 79(4), 606–623. https://doi.org/10.1086/354848
• Price, D. de S. (1976). A general theory of bibliometric and other cumulative advantage processes. Journal of the American Society for Information Science, 27(5), 292–306. https://doi.org/10.1002/asi.4630270505
• Allison, P. D., Long, J. S., & Krauze, T. K. (1982). Cumulative advantage and inequality in science. American Sociological Review, 47(5), 615–625. https://doi.org/10.2307/2095162
• DiPrete, T. A., & Eirich, G. M. (2006). Cumulative advantage as a mechanism for inequality: A review of theoretical and empirical developments. Annual Review of Sociology, 32, 271–297. https://doi.org/10.1146/annurev.soc.32.061604.123127
• Bask, M., & Bask, M. (2015). Cumulative (dis)advantage and the Matthew effect in life-course analysis. PLOS ONE, 10(11), e0142447. https://doi.org/10.1371/journal.pone.0142447

Life course and health

• Dannefer, D. (2003). Cumulative advantage/disadvantage and the life course: Cross-fertilizing age and social science theory. The Journals of Gerontology: Series B, 58(6), S327–S337. https://doi.org/10.1093/geronb/58.6.S327
• O’Rand, A. M. (1996). The precious and the precocious: Understanding cumulative disadvantage and cumulative advantage over the life course. The Gerontologist, 36(2), 230–238. https://doi.org/10.1093/geront/36.2.230
• Ross, C. E., & Wu, C.-L. (1996). Education, age, and the cumulative advantage in health. Journal of Health and Social Behavior, 37(1), 104–120. https://doi.org/10.2307/2137234
• Ferraro, K. F., & Shippee, T. P. (2009). Aging and cumulative inequality: How does inequality get under the skin? The Gerontologist, 49(3), 333–343. https://doi.org/10.1093/geront/gnp034
• Leopold, L., & Engelhardt, H. (2013). Education and physical health trajectories in old age: Evidence from the Survey of Health, Ageing and Retirement in Europe (SHARE). International Journal of Public Health, 58(1), 23–31. https://doi.org/10.1007/s00038-012-0399-0

Causal identification

• van de Rijt, A., Kang, S. M., Restivo, M., & Patil, A. (2014). Field experiments of success-breeds-success dynamics. Proceedings of the National Academy of Sciences, 111(19), 6934–6939. https://doi.org/10.1073/pnas.1316836111
• Restivo, M., & van de Rijt, A. (2012). Experimental study of informal rewards in peer production. PLOS ONE, 7(3), e34358. https://doi.org/10.1371/journal.pone.0034358
• Salganik, M. J., Dodds, P. S., & Watts, D. J. (2006). Experimental study of inequality and unpredictability in an artificial cultural market. Science, 311(5762), 854–856. https://doi.org/10.1126/science.1121066
• Bol, T., de Vaan, M., & van de Rijt, A. (2018). The Matthew effect in science funding. Proceedings of the National Academy of Sciences, 115(19), 4887–4890. https://doi.org/10.1073/pnas.1719557115
• Azoulay, P., Stuart, T., & Wang, Y. (2014). Matthew: Effect or fable? Management Science, 60(1), 92–109. https://doi.org/10.1287/mnsc.2013.1755
• Simcoe, T. S., & Waguespack, D. M. (2011). Status, quality, and attention: What’s in a (missing) name? Management Science, 57(2), 274–290. https://doi.org/10.1287/mnsc.1100.1270
• Wang, Y., Jones, B. F., & Wang, D. (2019). Early-career setback and future career impact. Nature Communications, 10, 4331. https://doi.org/10.1038/s41467-019-12189-3
• Jacob, B. A., & Lefgren, L. (2011). The impact of research grant funding on scientific productivity. Journal of Public Economics, 95(9–10), 1168–1177. https://doi.org/10.1016/j.jpubeco.2011.05.005
• Borjas, G. J., & Doran, K. B. (2015). Prizes and productivity: How winning the Fields Medal affects scientific output. Journal of Human Resources, 50(3), 728–758. https://doi.org/10.3368/jhr.50.3.728

Education and development

• Stanovich, K. E. (1986). Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy. Reading Research Quarterly, 21(4), 360–407. https://doi.org/10.1598/RRQ.21.4.1
• Pfost, M., Hattie, J., Dörfler, T., & Artelt, C. (2014). Individual differences in reading development: A review of 25 years of empirical research on Matthew effects in reading. Review of Educational Research, 84(2), 203–244. https://doi.org/10.3102/0034654313509492
• Cunha, F., & Heckman, J. (2007). The technology of skill formation. American Economic Review, 97(2), 31–47. https://doi.org/10.1257/aer.97.2.31
• Harden, K. P., Domingue, B. W., Belsky, D. W., Boardman, J. D., Crosnoe, R., Malanchini, M., Nivard, M., Tucker-Drob, E. M., & Harris, K. M. (2020). Genetic associations with mathematics tracking and persistence in secondary school. npj Science of Learning, 5, 1. https://doi.org/10.1038/s41539-020-0060-2
• Knigge, A., Maas, I., Stienstra, K., de Zeeuw, E. L., & Boomsma, D. I. (2022). Delayed tracking and inequality of opportunity: Gene-environment interactions in educational attainment. npj Science of Learning, 7, 6. https://doi.org/10.1038/s41539-022-00122-1
• Jussim, L., & Harber, K. D. (2005). Teacher expectations and self-fulfilling prophecies: Knowns and unknowns, resolved and unresolved controversies. Personality and Social Psychology Review, 9(2), 131–155. https://doi.org/10.1207/s15327957pspr0902_3

Relative age effect

• Musch, J., & Grondin, S. (2001). Unequal competition as an impediment to personal development: A review of the relative age effect in sport. Developmental Review, 21(2), 147–167. https://doi.org/10.1006/drev.2000.0516
• Bedard, K., & Dhuey, E. (2006). The persistence of early childhood maturity: International evidence of long-run age effects. Quarterly Journal of Economics, 121(4), 1437–1472. https://doi.org/10.1093/qje/121.4.1437
• Campbell, T. (2014). Stratified at seven: In-class ability grouping and the relative age effect. British Educational Research Journal, 40(5), 749–771. https://doi.org/10.1002/berj.3127
• Black, S. E., Devereux, P. J., & Salvanes, K. G. (2011). Too young to leave the nest? The effects of school starting age. Review of Economics and Statistics, 93(2), 455–467. https://doi.org/10.1162/rest_a_00081

Networks and distributions

• Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512. https://doi.org/10.1126/science.286.5439.509
• Petersen, A. M., Jung, W.-S., Yang, J.-S., & Stanley, H. E. (2011). Quantitative and empirical demonstration of the Matthew effect in a study of career longevity. Proceedings of the National Academy of Sciences, 108(1), 18–23. https://doi.org/10.1073/pnas.1016733108
• Pluchino, A., Biondo, A. E., & Rapisarda, A. (2018). Talent versus luck: The role of randomness in success and failure. Advances in Complex Systems, 21(3–4), 1850014. https://doi.org/10.1142/S0219525918500145

Counterevidence and limits

• Haworth, C. M. A., Wright, M. J., Luciano, M., Martin, N. G., de Geus, E. J. C., van Beijsterveldt, C. E. M., Bartels, M., Posthuma, D., Boomsma, D. I., Davis, O. S. P., Kovas, Y., Corley, R. P., DeFries, J. C., Hewitt, J. K., Olson, R. K., Rhea, S.-A., Wadsworth, S. J., Iacono, W. G., McGue, M., … Plomin, R. (2010). The heritability of general cognitive ability increases linearly from childhood to young adulthood. Molecular Psychiatry, 15(11), 1112–1120. https://doi.org/10.1038/mp.2009.55
• Dickens, W. T., & Flynn, J. R. (2001). Heritability estimates versus large environmental effects: The IQ paradox resolved. Psychological Review, 108(2), 346–369. https://doi.org/10.1037/0033-295X.108.2.346
• Rossiter, M. W. (1993). The Matthew Matilda effect in science. Social Studies of Science, 23(2), 325–341. https://doi.org/10.1177/030631293023002004