A Simple Model of Global Cascades on Random Networks¶
Watts, D. J. (2002). A Simple Model of Global Cascades on Random Networks. Proceedings of the National Academy of Sciences, 99(9), 5766-5771.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Cascade
- The defining commitment is sequential transmission through coupling: each affected element does not merely register the disturbance but becomes a new source of it, re-emitting the perturbation to elements that had not yet been reached.
This sourceThreshold model in which a node flips when the flipped fraction of its neighbors exceeds a threshold and then re-emits to its own neighbors, so small initial shocks can trigger large global cascades; identifies sub-critical vs super-critical regimes set by coupling density and threshold distribution and shows outcome magnitude is decoupled from trigger magnitude.
SupportedVerified against the work's full text
Watts's threshold model has switched-on nodes stay active and count toward their neighbours' thresholds, so activation spreads node to node through the network's links.
“nodes that are still in the off state can now have multiple (early-adopting) neighbors in the on state. Hence, even individuals that were originally classified as stable (the early and late majority) can now be toppled”
- The defining commitment is sequential transmission through coupling: each affected element does not merely register the disturbance but becomes a new source of it, re-emitting the perturbation to elements that had not yet been reached.
- Contagion
- Practitioners who recognize the shared structure can import a tested intervention from a foreign domain rather than reinventing it, which is the practical payoff of treating contagion as a single prime rather than as a set of unrelated domain phenomena.
This sourceThreshold model in which each affected node re-emits to its neighbors, so small initial shocks can trigger large global cascades; identifies the sub-critical/super-critical regimes separated by coupling density and threshold distribution, and shows outcome magnitude is decoupled from trigger magnitude.
- Practitioners who recognize the shared structure can import a tested intervention from a foreign domain rather than reinventing it, which is the practical payoff of treating contagion as a single prime rather than as a set of unrelated domain phenomena.
- Herding Behavior
- In political polling and election dynamics, reported poll standings influence voter behavior through bandwagon effects; late-decider studies in U.S. presidential elections repeatedly find this pattern, with voters updating toward perceived frontrunners more than fundamental data would justify.
This sourceThreshold model in which each affected node re-emits to its neighbors, so small initial shocks can trigger large global cascades; identifies the sub-critical/super-critical regimes separated by coupling density and threshold distribution, and shows outcome magnitude is decoupled from trigger magnitude.
- In political polling and election dynamics, reported poll standings influence voter behavior through bandwagon effects; late-decider studies in U.S. presidential elections repeatedly find this pattern, with voters updating toward perceived frontrunners more than fundamental data would justify.
- Information Cascade
- A core function of "information cascade" is to distinguish between genuine information aggregation (many independent signals combining toward accurate consensus) and cascade conformity (early choices hiding information, collapsing diversity into false consensus), a distinction Watts (2002) formalized in his network model of global cascades.
This sourceThreshold model in which each affected node re-emits to its neighbors, so small initial shocks can trigger large global cascades; identifies the sub-critical/super-critical regimes separated by coupling density and threshold distribution, and shows outcome magnitude is decoupled from trigger magnitude.
Supported in partVerified against the work's full text
Watts describes information cascades as herd-like imitation of others' actions in a threshold network model; he does not formalise a contrast between genuine aggregation and false consensus.
“individuals in a population exhibit herd-like behavior because they are making decisions based on the actions of other individuals rather than relying on their own information about the problem”
- A core function of "information cascade" is to distinguish between genuine information aggregation (many independent signals combining toward accurate consensus) and cascade conformity (early choices hiding information, collapsing diversity into false consensus), a distinction Watts (2002) formalized in his network model of global cascades.
- Percolation Threshold
- Granovetter's threshold models of collective behaviour and Watts's cascade models carried the percolation framework — backbone, critical cluster, and all — into social dynamics.
This sourceCarries the percolation framework (critical cluster, giant component) into social cascade dynamics on networks.
Supported in partVerified against the work's full text
Watts reduces global cascades to a percolation problem on the vulnerable cluster with two phase transitions; he does not credit Granovetter with importing percolation or use 'backbone'.
“the subnetwork of vulnerable vertices must percolate”
- Granovetter's threshold models of collective behaviour and Watts's cascade models carried the percolation framework — backbone, critical cluster, and all — into social dynamics.
- Propagation
- What amplifies the signal, and what dampens it, as Watts (2002) demonstrates by showing that cascade behavior depends on network connectivity rather than the triggering event alone?
This sourceThreshold model in which each affected node re-emits to its neighbors, so small initial shocks can trigger large global cascades; identifies the sub-critical/super-critical regimes separated by coupling density and threshold distribution, and shows outcome magnitude is decoupled from trigger magnitude.
SupportedVerified against the work's full text
Watts reports a two-regime result: where the network of interpersonal influences is sparse, “the propagation of cascades is limited by the global connectivity of the network”, and where it is dense, propagation is limited instead by the stability of the individual nodes. The cascades at issue are large but rare ones set off by small initial shocks, so what a cascade reaches depends on the structure it spreads through rather than on the trigger alone. The work does not quantify amplification or damping of a signal; that vocabulary is the article's rendering of a threshold-cascade result.
“When the network of interpersonal influences is sufficiently sparse, the propagation of cascades is limited by the global connectivity of the network; and when it is sufficiently dense, cascade propagation is limited by the stability of the individual nodes.”
- What amplifies the signal, and what dampens it, as Watts (2002) demonstrates by showing that cascade behavior depends on network connectivity rather than the triggering event alone?
- Systemic Risk
- Recognizing the pattern enables reasoning about contagion paths, critical (too-connected-to-fail) nodes, the difference between robust-yet-fragile architectures, and why adding connections can raise both efficiency and systemic vulnerability simultaneously.
This sourceThreshold model in which each affected node re-emits to its neighbors, so small initial shocks can trigger large global cascades; identifies the sub-critical/super-critical regimes separated by coupling density and threshold distribution, and shows outcome magnitude is decoupled from trigger magnitude.
Supported in partVerified against the work's full text
Watts supports critical highly connected nodes and an explicit robust-yet-fragile regime; "efficiency" and the connections-raise-vulnerability claim are only partly or not supported.
“and the most highly connected nodes are critical in triggering cascades. In the second case, the distribution of cascades is bimodal, and nodes with average connectivity, by virtue of their greater frequency, are much more likely to serve as triggers. In the latter regime, the system displays a more dramatic kind of robust-yet-fragile quality”
- Recognizing the pattern enables reasoning about contagion paths, critical (too-connected-to-fail) nodes, the difference between robust-yet-fragile architectures, and why adding connections can raise both efficiency and systemic vulnerability simultaneously.
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