I feel like we may be talking about different things then. I was referring to open/boundary edges (shown in light blue in component mode) if you are trying to get rid of a doubled up edge loop i would suggest that it would be easier to select a single edge loop with double click or alt+MMB click to select one of the two loops and delete it.
To merge edges the way you are asking about though is a bit tougher. it can be done by selecting the edge ring (not the loops but the ring between them) to do this select an edge along the ring, then shift double click an adjacent ring edge or alt+MMB and adjacent ring edge with the same initial selection. (Softimage recently added more Maya friendly double clicking to all the selection tools sorry) Then Collapse components or Ctrl+Del (the one below insert),
This can be done on single edges, multiple verts, edge rings and faces, it’s basically a merge to center so be careful with your selections. And as ThE_JacO said the tweak tool is awesome with merge.
As for double edges, thats a tricky one, it used to be that Softimage got testy and would warn you for trying to build double edges, now i’m trying to test it and I can’t even make one. That said I really suggest not modeling with double edges, in a situation where all you need is a sharp line just intersect the geo. Or if you want a smooth transition you can open a hole up and weld whatever it is with the boundary (distance based) merge tools.