Lustick, Miodownik / Neighborhoods and Tips
39
Young, H. Peyton. 1999. “Diffusion in Social Networks.” CSED Working Paper 2.
Brookings Institution.
1
Thus “tipping" is distinguished from other patterns that could also be coded as "non-linear," sudden, or
drastic. If a crowd of people simultaneously raise umbrellas when rain begins to fall it would count as a
sudden change in collective behavior, but we would code it as a "flip," not a "tip" or cascade. It is a flip
instead of a tip because the pattern of change does not radiate out from a particular point or set of points in
the social space. In this case, each individual's change of state is prompted by a stimulus exogenous to the
entire group and is identical and simultaneous in its impact on every member of the collective. On the
other hand, should we observe individuals in a crowd raising umbrellas when it is not raining, we might
well hypothesize that a cascade of conformity was occurring such that individuals, prompted by
inclinations to imitate their umbrella covered neighbors, were producing, by their behavior, an accelerating
and widening pattern of umbrella-raising.
2
For example, many suburbanites can have regular contacts with their workmates in the city, and barely
ever meet the people who live across the street from them. It is worth emphasizing that representations of
networks may appear “geographical” without reflecting a geographical proximity principle or dimension of
contact as operative.
3
For a useful meta-study of research on cascades see Bikchandani, Hirshleifer, and Welch (1998).
4
The principle of equilibrium has been a powerfully attractive force in the social sciences. It promises that
at some strategic level of analysis soluble equations can capture steady realities. For systems dominated by
non-conscious or non-rational elements equilibrium is achieved by homeostatic processes. When beings
endowed with intentionality are imagined as the key elements in a system, “negative feedback” is called
upon as the mechanism which keeps the system in equilibrium, or almost always moving toward it. For a
discussion contrasting the role of equilibrium in rational choice theory to that of “emergence” in agent-
based modeling approaches see Johnson (1998). Concerning the peculiar cross-disciplinary force of the
equilibrium idea in Western natural science and science see Murphy (1996). For arguments about the
crucial, but severely under-explored role in economics of positive feedback cycles and its methodological
implications see especially Arthur (1994); and David (1985).
5
For computer assisted explorations of Schelling’s model, which confirm and elaborate his results, see
Epstein and Axtell (1996).
6
For example, the Bikchandani, Hirshleifer, and Welch (1998, p. 159) meta-study includes just one brief
paragraph on one study focused on this variable, and that simply suggests that an innovation perceived as
valuable will spread more rapidly if each potential adopter monitors two, rather than one, other potential
adopter.
7
See for examples in the ethnographies presented in Chapters 5 and 6, “Family Strategies in Response to
the Cataclysm” and “If Not Assimilation, Then What?” in Laitin (1998), pp. 105-198.
8
Somer uses the notion of each individual’s “expected public utility” of acting in conformance with private
(non-ethnicized) preferences vs. public (ethnicized) preferences. The key role played by this concept in his
formalized threshold model points to the importance of the spatiality variable (In what different ways and
with what different effects might boundedly rational individuals assess expected public utilities?), even as
the mechanism translating public behavior into private assessments is left entirely unexamined.
9
Spin-glass models expect some specific pattern of disorderliness in the configuration of individuals
“activated” on state A or state B at time 0. The attempt is then made to infer, from this specific case or from
samples of parallel cases, properties associated with the type of system they instantiate. This abstract
categorization of the problem often animates efforts to assess the propensities of social systems to move
from a disequilibrated to an equilibrated state. The most common rendering of this problem as it pertains to
our consideration of spatiality and tipping figures is as a coordination game played by a population of
interacting agents as activated on one of two available states. Questions are then asked about the
conditions under which the behavior of agents in the population will converge on one of the two states.
Answers to these questions are sought by combining generalizations from intuitions about how small parts
of the array would behave under different conditions, formulas to capture the impact of those conditions
tractable to algebraic expression, and numerical simulations to explore the robustness of hypotheses linking
parametric specifications to “mean field” expectations—predictions about how, on average, particular
versions of these systems will behave. For an on point discussion see Axtell (2003).
Convention