Gong, Jyh-Chyi; PhD
UNIVERSITY OF CALIFORNIA, SAN DIEGO, 1997
ECONOMICS, THEORY (0511); SOCIOLOGY, THEORY AND METHODS (0344)
In this dissertation a variety of social interaction dynamics are studied concerning
the question of how
conventions come to be established. In chapter I, each person is characterized
by his or her probability of
adhering to the norm. At random, people observe the adherence behavior of others
and, from period to
period, adjust their own adherence probabilities in a corresponding direction.
In a main case of the
model, the distribution of adherence probabilities gradually evolves upward
or downward, depending on
initial conditions, until the population is in strong (possibly unanimous) conformity
with the norm or in
strong rejection of it. In other cases of the model, there is a single stable
equilibrium (either adherence to
or rejection of the norm). The population is infinite (a continuum) and the
social network displays 'uniform
global interaction'. In contrast, the other two chapters assume a finite population
and a much more
general social network. In Chapter II, various existing models and new variants
are discussed within a
common mathematical framework. The emphasis is on highly general social networks
and on various
combinations of individual adjustment ingredients--imitation, purely random
choice, thresholds, pure and
mixed action rules, linear and nonlinear responses, and so on. The standard
network assumptions in the
literature are uniform global interaction and near neighbor lattices. A series
of theorems demonstrates
that results on evolution to unanimity are robust to much broader network specifications.
In Chapter III, we
analyze deterministic and random versions of a threshold model. In the deterministic
version, we identify
a class of interaction structures--'radius uniform interaction'--which leads
to unanimity. The radius uniform
pattern is more general than uniform global interaction and uniform near neighbor
interaction on a lattice.
In the random version, we consider the two most common types of randomness--'log-linear'
and
'mistakes.' In each case, we provide substantial generalizations of the interaction
patterns under which
unanimity results hold.
Social
Systems Simulation Group
P.O. Box 6904 San Diego, CA 92166-0904 Roland Werner, Principal Phone/FAX (619) 660-1603 |