  We consider Vickrey-Clarke-Groves (VCG) auctions for a very general
combinatorial structure, in an average-case setting where item costs are
independent, identically distributed uniform random variables. We prove that
the expected VCG cost is at least double the expected nominal cost, and exactly
double when the desired structure is a basis of a bridgeless matroid. In the
matroid case we further show that, conditioned upon the VCG cost, the
expectation of the nominal cost is exactly half the VCG cost, and we show
several results on variances and covariances among the nominal cost, the VCG
cost, and related quantities. As an application, we find the asymptotic
variance of the VCG cost of the minimum spanning tree in a complete graph with
random edge costs.
