  The Lyapunov exponent for collective motion is defined in order to
characterize chaotic properties of collective motion for large populations of
chaotic elements. Numerical computations for this quantity suggest that such
collective motion is always chaotic, whenever it appears. Chaotic behavior of
collective motion is found to be confined within a small scale, whose size is
estimated using the value of the Lyapunov exponent. Finally, we conjecture why
the collective motion appears low dimensional despite the actual high
dimensionality of the dynamics.
