  We present numerical results on a complex dynamical model for the aggregation
of many individual rankings of S alternatives by the pairwise majority rule
under a deliberative scenario. Agents are assumed to interact when the Kemeny
distance between their rankings is smaller than a range R. The main object of
interest is the probability that the aggregate (social) ranking is transitive
as a function of the interaction range. This quantity is known to decay fast as
S increases in the non-interacting case. Here we find that when S>4 such a
probability attains a sharp maximum when the interaction range is sufficiently
large, in which case it significantly exceeds the corresponding value for a
non-interacting system. Furthermore, the situation improves upon increasing S.
A possible microscopic mechanism leading to this counterintuitive result is
proposed and investigated.
