  The collective coordination of distributed tasks in a complex system can be
represented as decision dynamics on a graph. This abstract representation
allows studying the performance of local decision heuristics as a function of
task complexity and network architecture. Here we identify hard-to-solve and
easy-to-solve networks in a social differentiation task within the basic model
of small-world graphs. We show that, depending on the details of the decision
heuristic as well as the length of the added links, shortcuts can serve as
structural promotors, which speed up convergence towards a solution, but also
as structural insulators, which make the network more difficult to solve. Our
findings have implications for situations where, in distributed decision
systems, regional solutions emerge, which are globally incompatible as for
example during the emergence of technological standards.
