This paper proposes a model and theory of leadership emergence whereby (1) small social groups are modeled as small-world networks and a betweeness metric is shown to be a property of networks with strong leadership, and (2) a theory of group formation based on stigmergy explains how such networks evolve and form. Specifically, dominant actors are observed to emerge from simulations of artificial termites constructing a wood chip network in a random walk, suggesting a correlation between various preferential attachment rules and emergent network topologies. Three attachment rules are studied: maximizing node betweeness (intermediary power), maximizing node degree (node connectivity), and limiting radius (size of the network in terms of network distance). The simulation results suggest that a preference for maximizing betweeness produces networks with a structure similar to the 62-node 9-11 terrorist network. Further simulations of emergent networks with small-world properties (a small radius) and high betweeness centrality (strong leader) are shown to match the topological structure of the 9-11 terrorist network, also. Interestingly, the same properties are not found in a small sampling of human-made physical infrastructure networks such as power grids, transportation systems, water and pipeline networks, suggesting a difference between social network emergence and physical infrastructure emergence. Additionally, a contagion model is applied to random and structured networks to understand the dynamics of anti-leader sentiment (uprisings and counter-movements that challenge the status quo). For random networks, simulated pro-leader (pro-government) and anti-leader (pro-rebel) sentiments are propagated throughout a social network like opposing diseases to determine which sentiment eventually prevails. Simulations of the rise of rebel sentiment versus the ratio of rebel to government sentiment show that rebel sentiment rises on less than 100% rebel/government sentiment when government sentiment is high (strong leadership), but requires greater than 100% rebel/government sentiment when government sentiment is low (weak leadership). However, when applied to the structured 9-11 terrorist network, rebel sentiment is slow to rise against strong leadership, because of the high betweeness structure of the 9-11 network. These results suggest a theory of how and why human stigmergy evolves networks with strong leaders, and why successful social networks are resilient against anti-leader sentiment. The author concludes that a combination of small world and high betweeness structure explain how social networks emerge strong leadership structure and why the resulting networks are resilient against being overthrown by a dissenting majority.
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