A Shortcut to Efficiency? Implications of the Small but Stratified World

Small World research (Watts and Strogatz 1998) has shown that “rewiring” just a few ties to be shortcuts across an otherwise clustered network structure results in a dramatic decline in the average distance between nodes but has only a modest effect on the degree of clustering. Accordingly, Small World structures seem to strike an attractive balance between two social goals: efficiency and community. But we show that the purported efficiency gains of the Small World may not be realized, even when the “contagions” being transmitted are quite “simple” (cf., Centola and Macy 2007). The problem is that Small Worlds rely on a small number of middlemen and are thus highly stratified. We show that structural inequality in Small World graphs can lead to dramatic outcome inequality, as reflected in the returns that actors receive from exchanging information with each other. And we show that this outcome inequality characteristic of the Small World also makes such structures inefficient when: (a) actors will not transmit valuable resources without getting equal value in return; and/or (b) actors are limited in their capacities for transmission. Under these very general conditions and especially in the connected structures studied in Small World research, the efficiency gains from the Small World are “hogged” by a small number of middlemen positioned on the shortcuts, who act as bottlenecks and thereby cause most others to do worse than in a more clustered structure. Our analysis thus demonstrates that the trade-off between efficiency and community is difficult to avoid, and the culprit is inequality.