Lustick, Miodownik / Neighborhoods and Tips
19
With regard to spatiality, Watts‘s (2003) most interesting finding is that if the
average size of neighborhoods is not too small and not too large, and if the average
propensity of any one agent in any part of the network to change state is not too small,
then global cascades are possible, with the conditions under which this is possible
narrowing as the average neighborhood size decreases (pp. 241-243). In terms of our
variable of spatiality, this finding suggests that convergence to a global cascade would
tend to be discouraged under a variety of connectivity conditions as the average size of
the neighborhoods comprising the network decreases. Note that this finding would
appear to run contrary to the claims of Ellison and Young, that reducing the size of local
clusters of interaction increases the rate of convergence. That is interesting in itself and
implies the need, via empirical studies or simulation, to test these conflicting
expectations. In any case, since we seek to understand the relationship between spatiality
and the likelihood of global cascades, and not whether under stated conditions a global
cascade is possible (regardless of how unlikely), this approach is limited in its usefulness.
The work on small worlds is also limited in its usefulness for the study of political
cascades because of assumptions it makes that are tied to traditions of research in
computer science and epidemiology. These traditions imagine switches that may or may
not turn on, of people who may or may not become infected, and of agents incapable of
changing their state back once it has changed. One problem with this kind of model is
that it encourages images of networks in which all but a small number of switches are off
or all but a small number of people are healthy. Assumptions of extreme sensitivity to a
signal to turn on or to exposure to an infected person (no matter how many healthy
persons one is also exposed to) resemble assumptions contained in Noelle-Neumann’s
Convention