  An essential task of groups is to provide efficient solutions for the complex
problems they face. Indeed, considerable efforts have been devoted to the
question of collective decision-making related to problems involving a single
dominant feature. Here we introduce a quantitative formalism for finding the
optimal distribution of the group members' competences in the more typical case
when the underlying problem is complex, i.e., multidimensional. Thus, we
consider teams that are aiming at obtaining the best possible answer to a
problem having a number of independent sub-problems. Our approach is based on a
generic scheme for the process of evaluating the proposed solutions (i.e.,
negotiation). We demonstrate that the best performing groups have at least one
specialist for each sub-problem -- but a far less intuitive result is that
finding the optimal solution by the interacting group members requires that the
specialists also have some insight into the sub-problems beyond their unique
field(s). We present empirical results obtained by using a large-scale database
of citations being in good agreement with the above theory. The framework we
have developed can easily be adapted to a variety of realistic situations since
taking into account the weights of the sub-problems, the opinions or the
relations of the group is straightforward. Consequently, our method can be used
in several contexts, especially when the optimal composition of a group of
decision-makers is designed.
