  Capacities on a finite set are sets functions vanishing on the empty set and
being monotonic w.r.t. inclusion. Since the set of capacities is an order
polytope, the problem of randomly generating capacities amounts to generating
all linear extensions of the Boolean lattice. This problem is known to be
intractable even as soon as $n>5$, therefore approximate methods have been
proposed, most notably one based on Markov chains. Although quite accurate,
this method is time consuming. In this paper, we propose the 2-layer
approximation method, which generates a subset of linear extensions,
eliminating those with very low probability. We show that our method has
similar performance compared to the Markov chain but is much less time
consuming.
