When Do Matthew Effects Occur?

Abstract

What are the boundary conditions of the Matthew Effect? In other words, under what circumstances do initial status differences result in highly skewed reward distributions over the long run, and when, conversely, is the accumulation of status-based advantages constrained? Using a formal model, we investigate the fates of actors in a contest who start off as status-equivalents, produce at different levels of quality, and thus come to occupy distinct locations in a status ordering. We build from a set of equations in which failing to observe cumulative advantage seems implausible and then demonstrate that, despite initial conditions designed to lead inevitably to status monopolization, circumstances still exist that rein in the Matthew Effect. Our results highlight the importance of a single factor governing whether the Matthew Effect operates freely or is circumscribed. This factor is the degree to which status diffuses through social relations. When actors’ status levels are strongly influenced by the status levels of those dispensing recognition to them, then eventually the top-ranked actor is nearly matched in status by the lower-ranked actor she endorses. In contrast, when actors’ status levels are unaffected by the status levels of those giving them recognition, the top-ranked actor amasses virtually all status available in the system. Our primary contribution is the intuition that elites may unwittingly and paradoxically destroy their cumulative advantage beneath the weight of their endorsements of others. Consequently, we find that the Matthew Effect is curtailed by a process that, at least in some social settings, is a property of status itself—its propensity to diffuse through social relations. Implications for future research are discussed.

Keywords:

• leadership
• social networks
• status

ACKNOWLEDGMENTS

Financial support from the University of Chicago Booth School of Business, the Ewing Marion Kauffman Foundation, and the National Research Foundation of Korea (2007-411-J01601, 2007-411-J01602) is gratefully acknowledged. We thank Rakesh Khurana, Michael Macy, Damon Phillips, and Ezra Zuckerman for particularly valuable comments.

Notes

¹For the micro-level version of the Matthew Effect, see Merton (1968, pp. 57–58), and for the macro-level version, see Merton (1968, p. 62). The term was derived from Saint Matthew's Gospel (25:29): “For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath.”

²An important exception is Podolny's (1993) compelling discussion of emergent status-erosion as the consequence of a high-status organization's choice to expand in market share by encroaching on a lower-status competitor's niche.

³Zuckerman and Kim's (2003) discussion of low-status consumers’ distaste for high-status producers for fear of the latter's lack of commitment to the former offers an intriguing additional constraint on the Matthew Effect: “consumers may sometimes regard high-status entrants as overqualified for low-status niches—that is, they are rejected because consumers are skeptical that they will be sufficiently committed to serving the niche. Put more prosaically, high-status producers who are perceived as ‘slumming’ or ‘carpet-bagging’ are likely to be rejected” (p. 30). The mechanism to which Zuckerman and Kim call attention is a bridle on cumulative advantage that could be discussed as predetermined or emergent—depending on one's priors about the capacity of locally evolving dispersions in status to alter preferences for interaction across large divides.

⁴Very briefly, two additional points merit attention. First, which of these inputs best corresponds to the status-conferring flow we have termed recognition will of course vary by empirical setting. Second, we do not assume that these acts of recognition are necessarily “genuine.” We are agnostic with respect to motive. That is, recognition can be strategic or feigned rather than earnest, and yet prove consequential in W.I. Thomas's sense.

⁵The solution to Eq. (1) in matrix form is S _t (α, β) = α(I − βR _t )⁻¹ R _t 1, where I is an identity matrix.

⁶ was set to zero in our simulations when any of these conditions was met: S _it  = 0; ; or q ²/4 + p ³/27 < 0. The latter, which requires the square root of a negative number, can occur for extremely small values of status (e.g., two actors for whom S _it  < 10⁻¹² met this condition in the simulations used to generate Fig. 3).

⁷Although it would be straightforward to add an error term to the recognition function, we maintain the existing formulation for simplicity. In addition, although this decision eliminates a source of the “looseness” of the linkage between quality and status (Podolny, 1993), it has the advantage of making it harder to rein in the Matthew Effect. Of course, the Matthew Effect will always fail to unfold in communication systems fraught with extreme noise (cf. Merton, 1968), where current quality—typically made easier to achieve by prior status—will necessarily never strongly affect future status.

⁸To use an example from the academic sphere, this is particularly true for colleagues who have the unfortunate habit of describing each newly-minting doctoral candidate for whom they write as among the top three students they have ever supervised. A fixed effect for such letter writers is implicitly estimated.

⁹So that actors start the contest as status-equivalents—with status S _it equal to unity for all i in the first round—we assigned 1/(n − 1) to the off-diagonal entries in the recognition matrix R _t at t = 1. Consequently, the only differentiator at the onset is ability A _i . Variations in ability give rise to distinct levels of quality Q _it at t = 1 from Eq. (6). After differences in Q _it arise, these then bring about differences in flows of recognition in the matrix R _t at t = 2, according to Eq. (7). Therefore, by the second round, actors differ in status. When t = 1, the two multipliers preceding Q _it in Eq. (7)—R _ijt and S _it —both necessarily equal unity, exerting no effect until actual acts of dispensing recognition have occurred and differences in status have therefore surfaced by t = 2.

¹⁰Our discussion of status diffusion raises the question of how the latter differs from Podolny's (2005) intriguing notion of status leakage: “In my conception, the fundamental check on the Matthew Effect is that high-status actors fear a loss of status due to any association with the low-status actors. Were it not for the risk of their status leaking through exchange relations, the high-status actors would permeate all market niches” (p. 37). Thus, in Podolny's model, a top-ranked actor suffers, or fears suffering, a status decline after affiliating with (and thus being stained by) a lower-ranked actor—for example, an elite company declines in status after associating with (or entering the niche of) a less well-regarded company. In contrast, in our model, a top-ranked individual falls in status after endorsing (and thus abetting the ascent of) a lower-ranked actor—for instance, an elite leader suffers status loss through anointing, and then getting eclipsed by, a lieutenant. The approaches are similar in that status-spillovers occur in both accounts. The approaches differ in three main respects. First, our model more restrictively rests on a concrete endorsement, rather than affiliation or co-presence in the same market niche. Second, loss of status for the top-ranked actor probably occurs over a longer time-horizon in our approach. That is, entering the “wrong” niche may prove immediately status-corrosive, but suffering status loss as an anointed associate ascends may require more time. Third, elite actors are almost certainly more aware of the risk of status loss in Podolny's account than in ours. Put differently, while a firm is generally quite conscious of the penalty of moving down market (and thus may never make the move), in our approach a leader can be blindsided by the status mobility of a chosen follower.

¹¹We note that the multiplicative function in Eq. (7) for determining recognition does imply a caveat: If a focal individual were the only contestant possessing a positive status score (and thus the sole contestant capable of contributing a non-zero level of quality), this individual, by construction, could not show recognition to anyone. However, more than one contestant ended in steady-state with a non-zero level of status in all simulations.

¹²Going beyond the assumptions of our model, one can certainly imagine (especially in the “total institutions” just mentioned) situations in which the top-ranked actor never dispenses recognition to others, but nonetheless fails to preserve the Matthew Effect because of a lower-ranked actor who gains the support of those ranked even further down and initiates a coup. This possibility is consistent with Luhmann's (1987) preference-based constraint on the Matthew Effect, according to which individuals have strong desire for status mobility and turnover, and, more generally, with research underscoring lower-status actors’ heightened openness to social influence (Bothner, 2003; Barnett and Pontikes, 2008).