Ex ante prediction of cascade sizes on networks of agents facing binary   outcomes
  We consider in this paper the potential for ex ante prediction of the cascade size in a model of binary choice with externalities (Schelling 1973, Watts 2002). Agents are connected on a network and can be in one of two states of the world, 0 or 1. Initially, all are in state 0 and a small number of seeds are selected at random to switch to state1. A simple threshold rule specifies whether other agents switch subsequently. The cascade size (the percolation) is the proportion of all agents which eventually switches to state 1. We select information on the connectivity of the initial seeds, the connectivity of the agents to which they are connected, the thresholds of these latter agents, and the thresholds of the agents to which these are connected. We obtain results for random, small world and scale -free networks with different network parameters and numbers of initial seeds. The results are robust with respect to these factors. We perform least squares regression of the logit transformation of the cascade size (Hosmer and Lemeshow 1989) on these potential explanatory variables. We find considerable explanatory power for the ex ante prediction of cascade sizes. For the random networks, on average 32 per cent of the variance of the cascade sizes is explained, 40 per cent for the small world and 46 per cent for the scale-free. The connectivity variables are hardly ever significant in the regressions, whether relating to the seeds themselves or to the agents connected to the seeds. In contrast, the information on the thresholds of agents contains much more explanatory power. This supports the conjecture of Watts and Dodds (2007.) that large cascades are driven by a small mass of easily influenced agents. 
Paul Ormerod and Ellie Evans
cs.SI physics.soc-ph