What makes Individual I's a Collective We; Coordination mechanisms & costs

The collective effort exceeds the sum of its parts when individuals coordinate and regulate their activities and behaviors. This holds true even in self-organizing systems with open, voluntary participation where coordination occurs implicitly. Here, we analyze the non-functional actions of contributors, administrators, and bots on Wikipedia, categorizing them by their asymmetric authority: one-way oversight and two-way. This categorization helps us reveal comparable patterns. First, we find remarkably consistent scaling factors for each category relative to system size. Two-way coordination scales superlinearly (with an exponent of $1.3$), while oversight coordination grows sublinearly (with an exponent of $0.9$), suggesting an underlying mechanism for coordination across communities. Second, we identify the hierarchical modular structure of interactions as a key factor for the economy of scale in coordination, and we propose a mathematical model to explain these results. Finally, our temporal analysis shows a shift from two-way interactions to one-way oversight as system size increases. This suggests the emergence of a nascent hierarchical structure even in self-organizing systems, echoing Weber's theory of organizational evolution.