How groups reach consensus led by a few informed individuals
In plain words
In fish schools and bee swarms, a small fraction of informed members can steer the whole group to a target. How the needed fraction depends on group size, and how conflicting preferences are resolved, has had limited quantitative tests in natural groups.
Precise statement
In self-propelled particle models with a fraction $p$ of informed individuals biased toward a target, group heading accuracy depends on $p$ and $N$, and the required $p$ decreases as $N$ grows (Couzin and co-workers, 2005); with two informed subgroups preferring targets at angle $\theta$ apart, the group switches from averaging to choosing one target above a critical $\theta$. Measure $p_c(N)$ and the critical angle in natural groups and compare with model predictions.
What would settle it
Controlled experiments with trained or virtually informed individuals in groups of varying $N$ that measure $p_c(N)$ and the bifurcation angle.