  An interesting example for collective decision making is the so-called
Mexican wave during which the spectators in a stadium leap to their feet with
their arms up and then sit down again following those to their left (right)
with a small delay. Here we use a simple, but realistic model to explain how
the combination of the local and global interactions of the spectators produces
a breaking of the symmetry resulting in the replacement of the symmetric
solution -- containing two propagating waves -- by a single wave moving in one
of the two possible directions. Our model is based on and compared to the
extensive observations of volunteers filling out the related questionnaire we
have posted on the Internet. We find that, as a function of the parameter
controlling the strength of the global interactions, the transition to the
single wave solution has features reminiscent of discontinuous transitions.
After the spontaneous symmetry breaking the two directions of propagation are
still statistically equivalent. We investigate also how this remaining symmetry
is broken in real stadia by a small asymmetrical term in the perception of
spectators.
