  Social networks play an important role in analyzing the impact of
individual-level interactions on societal or economic outcomes. We model
interactive decision making for a community of individuals with different
traits, represented by a social network with trait-attributed nodes. We develop
a deterministic process generating a sequence of choices for each individual
based on a trait-attributed social network, initial choices of individuals and
a set of predetermined trait-dependent rules for making decisions. The object
of interest is the sequence of cumulative sum of choices over all individuals,
which we call the cumulative sequence and consider as an index of collective
decisions. We observe that, in a time period, a cumulative sequence can be
unpredictable or predictable showing a repeated pattern either escalating to an
extreme or constantly oscillating. We consider that predictable cumulative
sequences represent unstable collective decisions of communities either
extremizing or internally conflicting, while unpredictable cumulative sequences
show stable changes. We analyze the effects of network topology and trait
distribution on the probability of cumulative sequences being predictable,
escalating and oscillating by simulations. Our findings include that unstable
collective decisions are more probable as network density increases, that
centralized networks are more likely to have unstable collective decisions and
that networks with excessively clustered or scattered conformists and rebels
tend to produce unstable cumulative sequences. We discuss the potential of the
model as a framework for studying individuals with different traits on a social
network directly and indirectly interacting in decision making.

Physics and Society;Combinatorics