The origin of large but rare cascades that are triggered by small initial shocks is a problem that manifests itself in social and natural phenomena as diverse as cultural fads and innovations [1-3], social movements [4, 5], and cascading failures in large infrastructure networks [6-8]. Here we present a possible explanation of such cascades in terms of a network of interacting agents whose decisions are determined by the actions of their neighbors according to a simple threshold rule. We identify conditions under which the network is susceptible to very rare, but very large cascades and explain why such cascades may be difficult to anticipate in practice.
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Paper provided by Santa Fe Institute in its series Working Papers with number
00-12-062.