paper

Competitive Social Mobilization in Threshold Models of Collective Action

arXiv:2601.18682 · doi:10.1016/j.physa.2026.131642

Abstract

Social mobilization often fails not for a lack of collective interest, but because of fierce competition between rival movements for the same limited pool of participants. We generalize the classic threshold model of collective behavior to analyze this competitive aggregation, exploring how populations with diverse participation thresholds navigate multiple, mutually exclusive causes. Focusing on the conditions necessary for a single consensus movement to encompass an entire population, our analysis reveals that the outcome of social competition depends critically on the stability of individual dispositions. In quenched environments where participation thresholds are fixed, increasing resistance initially allows a dominant movement to suppress its competitors; however, further resistance triggers a sudden collapse into total fragmentation as low-threshold instigators become too rare to sustain growth. Conversely, in annealed environments where opinions are fluid, higher resistance paradoxically drives a winner-takes-all consensus. In this fluid scenario, massive movements can only be avoided through a deliberate divide-and-conquer strategy. In both cases, the transitions between pulverized and massive movements are discontinuous. These findings demonstrate that the effectiveness of social control depends entirely on environmental stability: raising the cost of participation can either forge unity or shatter collective action into insignificance.

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