I believe that if you're shooting instinctive, with the bow canted, eye domination is irrelevant (assuming that you keep both eyes open). The real problems begin when you shoot with a vertical bow (olympic style) with or without sights. If you're trying to line up the string with a non-dominant eye, you have to be absolutely sure that the dominant eye doesn't take over or you'll be off by a couple of feet (like freeman says, above). If you are trying to shoot with only your non-dominant eye, unless you use a patch or some such device to prevent the dominant eye from taking over, every once in a while you're going to shoot a real clunker.