  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.
