  A key question concerning collective decisions is whether a social system can
settle on the best available option when some members learn from others 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.
