  An approximate dual representation for non-Abelian lattice gauge theories in
terms of a new set of dynamical variables, the plaquette occupation numbers
(PONs) that are natural numbers, is discussed. They are the expansion indices
of the local series of the expansion of the Boltzmann factors for every
plaquette of the Yang-Mills action. After studying the constraints due to gauge
symmetry, the SU(2) gauge theory is solved using Monte Carlo simulations. For a
PONs configuration the weight factor is given by Haar-measure integrals over
all links whose integrands are products of powers of plaquettes. Herein,
updates are limited to changes of the PON at a plaquette or all PONs on a
coordinate plane. The Markov chain transition probabilities are computed
employing truncated maximal trees and the Metropolis algorithm. The algorithm
performance is investigated with different types of updates for the plaquette
mean value over a large range of $\beta$s. Using a $12^4$ lattice very good
agreement with a conventional heath bath algorithm is found for the strong and
weak coupling limits. Deviations from the latter being below 0.1% for $2.5 <
\beta < 3$. The mass of the lightest $J^{PC}=0^{++}$ glueball is evaluated and
reproduces the results found in the literature.
