  The threshold model is a simple but classic model of contagion spreading in
complex social systems. To capture the complex nature of social influencing we
investigate numerically and analytically the transition in the behavior of
threshold-limited cascades in the presence of multiple initiators as the
distribution of thresholds is varied between the two extreme cases of identical
thresholds and a uniform distribution. We accomplish this by employing a
truncated normal distribution of the nodes' thresholds and observe a
non-monotonic change in the cascade size as we vary the standard deviation.
Further, for a sufficiently large spread in the threshold distribution, the
tipping-point behavior of the social influencing process disappears and is
replaced by a smooth crossover governed by the size of initiator set. We
demonstrate that for a given size of the initiator set, there is a specific
variance of the threshold distribution for which an opinion spreads optimally.
Furthermore, in the case of synthetic graphs we show that the spread
asymptotically becomes independent of the system size, and that global cascades
can arise just by the addition of a single node to the initiator set.
