  In many domains of life, business and management, numerous problems are
addressed by small groups of individuals engaged in face-to-face discussions.
While research in social psychology has a long history of studying the
determinants of small group performances, the internal dynamics that govern a
group discussion is not yet well understood. Here, we rely on computational
methods based on network analyses and opinion dynamics to described how
individuals influence each other during a group discussion. We consider the
situation in which a small group of three individuals engages in a discussion
to solve an estimation task. We propose a model describing how group members
gradually influence each other and revise their judgments over the course of
the discussion. The main component of the model is an influence network - a
weighted, directed graph that determines the extent to which individuals
influence each other during the discussion. In simulations, we first study the
optimal structure of the influence network that yields the best group
performances. Then, we implement a social learning process by which individuals
adapt to the past performance of their peers, thereby affecting the structure
of the influence network in the long run. We explore the mechanisms underlying
the emergence of efficient or maladaptive networks and show that the influence
network can converge towards the optimal one, but only when individuals exhibit
a social discounting bias by downgrading the relative performances of their
peers. Finally, we find a late-speaker effect, whereby individuals who speak
later in the discussion are perceived more positively in the long run and are
thus more influential. The numerous predictions of the model can serve as a
basis for future experiments, and this work opens research on small group
discussion to computational social sciences.
