Lustick, Miodownik / Neighborhoods and Tips
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10
A similar conclusion, using similar techniques, that “herding (is) more likely with small sample sizes,” is
offered by Ellison and Fudenberg (1995).
11
Young (1999) available online at
http://www.brookings.org/dybdocroot/ES/dynamics/papers/diffusion/diffusion.htm
12
The density of a network is here taken to be the average number of neighbors included in each neighbor's
neighborhood. See Rolfe (manuscript 2004) for a useful review of the literature on density.
13
Both Young and Ellison refer to simulation results as supportive of their analytic and intuitive findings,
but neither provide details about these simulations.
14
See for example Ellison and Fudenberg (2003).
15
See for example, Latané, Nowak, and Liu (1994); Axelrod (1997); Lustick (2000).
16
Results were also robust across treatment conditions, unreported here, featuring larger arrays,
differential densities of agents within the array, and for arrays in which initializations included small
majorities of one activated color over another.
17
We have given consideration to the important question of the mechanisms at work that could account for
the patterns of cascades and tipping we have observed. For reasons of space, however, we can simply
mention that our explanation rests on an interaction between the size of zones of knowledge available to
agents and the regularity vs. irregularity of distributions of differently sized clusters. Tipping requires of
individuals that they experience imbalance in the signals they receive about their world. So combinations
of these two variables that lead more agents to experience imbalance more rapidly will tend to encourage
cascades toward tips.
Convention