  A key question concerning collective decisions is whether a collective
decision-making system can settle on the best available option when some
members learn socially instead of evaluating the options on their own. This
question is challenging to study, and previous research has reached mixed
conclusions, because collective decision outcomes depend on the insufficiently
understood complex system of cognitive strategies, task properties, and social
influence processes. This study integrates these complex interactions together
in one general yet partially analytically tractable mathematical framework
using a dynamical system model. In particular, it investigates how the
interplay of the proportion of social learners, the relative merit of options,
and the type of conformity response affect collective decision outcomes in a
binary choice. The model predicts that when the proportion of social learners
exceeds a critical threshold, a bi-stable state appears in which the majority
can end up favoring either the higher- or lower-merit option, depending on
fluctuations and initial conditions. Below this threshold, the high-merit
option is chosen by the majority. The critical threshold is determined by the
conformity response function and the relative merits of the two options. The
study helps reconcile disagreements about the effect of social learners on
collective performance and proposes a mathematical framework that can be
readily adapted to extensions investigating a wider variety of dynamics.
