The semidefinite programming algorithm by Goemans and Williamson (GW) guarantees a 0.878-approximation of MaxCut. If the UGC is true, this is the best approximation one can achieve unless NP=P.
For a graph G=(V,E) there exist 2^|V| possible cuts. Are there any results on how large the set of cuts is which are better the GW-approximation, i.e. $N(cuts_\mathrm{better})/2^{|V|}$. As MaxCut is NP, I would assume that this ratio should not be constant, but exponentially decreasing with the number of vertices. Is that intuition right and are there any results on that?