  We consider a Vicsek model of self-propelled particles with bounded
confidence, where each particle interacts only with neighbors that have a
similar direction. Depending on parameters, the system exhibits a continuous or
discontinuous polar phase transition from the isotropic phase to a phase with a
preferred direction. In a recent paper [1] the von Mises distribution was
proposed as an ansatz for polar ordering. In the present system the time
evolution of the angular distribution can be solved in Fourier space. We
compare the results of the Fourier analysis with the ones obtained by using the
von Mises distribution ansatz. In the latter case the qualitative behavior of
the system is recovered correctly. However, quantitatively there are serious
deviations. We introduce an extended von Mises distribution ansatz such that a
second term takes care of the next two Fourier modes. With the extended ansatz
we find much better quantitative agreement. As an alternative approach we also
use a Gaussian and a geometric series ansatz in Fourier space. The geometric
series ansatz is analytically handable but fails for very weak noise, the
Gaussian ansatz yields better results but it is not analytically treatable.
