I've used superglue (i.e. Cyanoacrylate) many, many times to affix plastic to cardboard, both the softish variety of 1/72 figures, as well as hard polystyrene. Works like a charm, although a hot glue gun would work as well - I'd stay clear of PVA as this doesn't provide a strong enough bond, and plastic glue won't work as it cannot dissolve the cardboard.