We model the dynamics of a variation of the Schelling model for agents described simply by
a continuously distributed variable—wealth. Agent movement is not dictated by agent
choice as in the classic Schelling model, but by their wealth status. Agents move to neighborhoods
where their wealth is not lesser than that of some proportion of their neighbors,
the threshold level. As in the case of the classic Schelling model, we find here that wealthbased
segregation occurs and persists. However, introducing uncertainty into the decision
to move—that is, with some probability, if agents are allowed to move even though the
threshold condition is contravened—we find that even for small proportions of such disallowed
moves, the dynamics no longer yield segregation but instead sharply transition into a
persistent mixed wealth distribution, consistent with empirical findings of Benenson, Hatna,
and Or. We investigate the nature of this sharp transformation, and find that it is because of
a non-linear relationship between allowed moves (moves where threshold condition is satisfied)
and disallowed moves (moves where it is not). For small increases in disallowed
moves, there is a rapid corresponding increase in allowed moves (before the rate of
increase tapers off and tends to zero), and it is the effect of this non-linearity on the dynamics
of the system that causes the rapid transition from a segregated to a mixed wealth state.
The contravention of the tolerance condition, sanctioning disallowed moves, could be interpreted
as public policy interventions to drive de-segregation. Our finding therefore suggests
that it might require limited, but continually implemented, public intervention—just sufficient
to enable a small, persistently sustained fraction of disallowed moves so as to trigger the
dynamics that drive the transformation from a segregated to mixed equilibrium.