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A Model of Robust Positions in Social Networks

Posted by admin in 2010 - (Comments Off on A Model of Robust Positions in Social Networks)

Matthew S. Bothner, Edward Bishop Smith, and Harrison C. White

What makes an actor’s position in social structure robust rather than fragile? This article introduces a network model that pictures occupants of robust positions as recipients of diversified support from durably located others, and portrays occupants of fragile positions as dependents on tenuously situated others. The model builds from Herfindahl’s measure of concentration and Bonacich’s (1987) measure of status. Using Newcomb’s panel study of status-conferring flows among members of a college fraternity, we find empirical support for the contention that fragility reduces future growth in status. Extensions of the model both to input-output networks among industries in the U.S. economy and to hiring networks among academic departments are presented. Implications for future research are discussed.

American Journal of Sociology, 116 (2010): 943-992

When Do Matthew Effects Occur?

Posted by admin in 2010 - (Comments Off on When Do Matthew Effects Occur?)

Matthew S. Bothner, Richard Haynes, Wonjae Lee, and Edward Bishop Smith

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.

Journal of Mathematical Sociology, 34 (2010): 80-114