  The movement of a flock with a single leader (and a directed path from it to
every agent) can be stabilized. Nonetheless for large flocks perturbations in
the movement of the leader may grow to a considerable size as they propagate
throughout the flock and before they die out over time. As an example we
consider a string of N+1 oscillators moving in the line. Each one `observes'
the relative velocity and position of only its nearest neighbors. This
information is then used to determine its own acceleration. Now we fix all
parameters except the number of oscillators. We then show (within a certain
class of systems) that a perturbation in the leader's orbit is almost always
amplified exponentially in N as it propagates towards the outlying members of
the flock. The only exception is when there is a symmetry present in the
interaction: in that case the growth of the perturbation is linear in N.
