This paper presents a model of global cascades on random networks, explaining how small initial shocks can trigger large, rare cascades in social, economic, and physical systems. The model considers a sparse, random network of interacting agents whose decisions are determined by the actions of their neighbors according to a simple threshold rule. Two regimes are identified in which the network is susceptible to very large cascades—global cascades—that occur very rarely. When cascade propagation is limited by the connectivity of the network, a power law distribution of cascade sizes is observed, analogous to the cluster size distribution in standard percolation theory and avalanches in self-organized criticality. But when the network is highly connected, cascade propagation is limited instead by the local stability of the nodes themselves, and the size distribution of cascades is bimodal, implying a more extreme kind of instability that is correspondingly harder to anticipate. The model is motivated by considering a population of individuals each of whom must decide between two alternative actions, and whose decisions depend explicitly on the actions of other members of the population. The model is based on a binary decision rule with externalities, where an individual agent observes the current states of k other agents and adopts state 1 if at least a threshold fraction φ of its k neighbors are in state 1, else it adopts state 0. The model is applied to a network of n agents, where each agent is connected to k neighbors with probability p_k and the average number of neighbors is ⟨k⟩ = z. The model is shown to be applicable to a wide range of systems, including social and economic systems, and physical infrastructure networks. The paper shows that the vulnerability of interconnected systems to global cascades depends on the network of interpersonal influences governing the information that individuals have about the world, and therefore their decisions. The model is analyzed using a generating function approach, and the results show that the cascade condition is a critical factor in determining whether global cascades occur. The cascade condition is interpreted as follows: when G_0'(1) < z, all vulnerable clusters in the network are small; hence, the early adopters are isolated from each other and will be unable to generate the momentum necessary for a cascade to become global. But when G_0'(1) > z, the typical size of vulnerable clusters is infinite, implying the presence of a percolating vulnerable cluster, in which case random initial shocks should trigger global cascades with finite probability. The paper concludes that global cascades in social and economic systems, as well as cascading failures in engineered networks, display two striking qualitative features: they occur rarely, but by definition are large when they do. The paper also shows that systemic heterogeneity has mixed effects on systemic stability. On the one hand, increased heterogeneity of individual thresholds appears to increase the likelihood of global cascades; but on the other hand, increased heterogeneity of vertex degree appears to reduce it. The paper hopes that the introduction ofThis paper presents a model of global cascades on random networks, explaining how small initial shocks can trigger large, rare cascades in social, economic, and physical systems. The model considers a sparse, random network of interacting agents whose decisions are determined by the actions of their neighbors according to a simple threshold rule. Two regimes are identified in which the network is susceptible to very large cascades—global cascades—that occur very rarely. When cascade propagation is limited by the connectivity of the network, a power law distribution of cascade sizes is observed, analogous to the cluster size distribution in standard percolation theory and avalanches in self-organized criticality. But when the network is highly connected, cascade propagation is limited instead by the local stability of the nodes themselves, and the size distribution of cascades is bimodal, implying a more extreme kind of instability that is correspondingly harder to anticipate. The model is motivated by considering a population of individuals each of whom must decide between two alternative actions, and whose decisions depend explicitly on the actions of other members of the population. The model is based on a binary decision rule with externalities, where an individual agent observes the current states of k other agents and adopts state 1 if at least a threshold fraction φ of its k neighbors are in state 1, else it adopts state 0. The model is applied to a network of n agents, where each agent is connected to k neighbors with probability p_k and the average number of neighbors is ⟨k⟩ = z. The model is shown to be applicable to a wide range of systems, including social and economic systems, and physical infrastructure networks. The paper shows that the vulnerability of interconnected systems to global cascades depends on the network of interpersonal influences governing the information that individuals have about the world, and therefore their decisions. The model is analyzed using a generating function approach, and the results show that the cascade condition is a critical factor in determining whether global cascades occur. The cascade condition is interpreted as follows: when G_0'(1) < z, all vulnerable clusters in the network are small; hence, the early adopters are isolated from each other and will be unable to generate the momentum necessary for a cascade to become global. But when G_0'(1) > z, the typical size of vulnerable clusters is infinite, implying the presence of a percolating vulnerable cluster, in which case random initial shocks should trigger global cascades with finite probability. The paper concludes that global cascades in social and economic systems, as well as cascading failures in engineered networks, display two striking qualitative features: they occur rarely, but by definition are large when they do. The paper also shows that systemic heterogeneity has mixed effects on systemic stability. On the one hand, increased heterogeneity of individual thresholds appears to increase the likelihood of global cascades; but on the other hand, increased heterogeneity of vertex degree appears to reduce it. The paper hopes that the introduction of