http://www.pnas.org/cgi/reprint/99/9/5766.pdf

Duncan Watts’ 2001 paper “A simple model of global cascades on random networks” analyzes the conditions under which global information cascades occur, using a simple model with varying parameters. A global information cascade is just a cascade that influences most of the nodes in a large network, initially formed by a small number of nodes starting in a novel ’state’. Similarly to one model we studied in class, Watts’ model consists of individuals in a network where each person observes the state of his neighbors and decides to enter state X if a certain threshold of his neighbors are in state X. Watts explored the global effect of using different thresholds for each individual, drawn from a particular distribution. He also used distributions to determine the number of neighbors that each individual has, and uses the parameter z to indicate the average number of neighbors each individual has. Watts analyzed cascades mathematically and eventually came up with a cascade condition, which is an equation that predicts when a cascade will occur in this simple model. He constructs a graph relating the threshold of each node, the average degree (# neighbors) of the nodes, and whether this combination had the capacity to form a global cascade. These cascades tended to form when each individual has a smaller number of neighbors, and when the threshold is low. His mathematical findings were supported by experimental data, using simulated networks with the same parameters. He found that when the network is not very well-connected, then the capacity for a global cascade to form is limited by the overall connectivity, and well-connected nodes are critical for global cascades to occur. When the network is well-connected, then the capacity for a global cascade is limited by the ’stability’ (threshold) of individual nodes. It is also interesting that this type of network seems very stable to various shocks applied to it, but dramatically and quickly cascades when the proper conditions are met. Another parameter that seemed to affect the likelihood of global cascades is the heterogeneity of thresholds and node degree. Watts found that when individual thresholds were diverse, global cascades were more likely to occur, but when the vertex degree of nodes was diverse, they were less likely to occur. I found many of these findings quite interesting and non-intuitive, and very applicable to the study of network theory. Large information cascades clearly have a huge effect on the decisions that people make every day, and their mechanism is not very well understood. Watts provides some basic analysis on the conditions under which global cascades are more likely to occur, and even though they are based on a simple model, they can definitely be insightful when analyzing and predicting real-world information cascades.