We study the effect of quantum fluctuations on the half-polarized
magnetization plateau of a pyrochlore antiferromagnet. We argue that an
expansion around the easy axis limit is appropriate for discussing the ground
state selection amongst the classically degenerate manifold of collinear states
with a 3:1 ratio of spins parallel/anti-parallel to the magnetization axis. A
general approach to the necessary degenerate perturbation theory is presented,
and an effective quantum dimer model within this degenerate manifold is derived
for arbitrary spin s. We also generalize the existing semiclassical analysis
of Hizi and Henley [Phys. Rev. B {\bf 73}, 054403 (2006)] to the easy axis
limit, and show that both approaches agree at large s. We show that under
rather general conditions, the first non-constant terms in the effective
Hamiltonian for s≥1 occur only at {\sl sixth} order in the transverse
exchange coupling. For s≥3/2, the effective Hamiltonian predicts a
magnetically ordered state. For s≤1 more exotic possibilities may be
realized, though an analytical solution of the resulting quantum dimer model is
not possible