I'm sorry, but you've completely missed the point. Nobody is talking about the "disparity in your happiness based on whether you knew the best strategy."
Obviously, if the honest approval ballot give me 9 utility points, and the strategy approval ballot gives me 10 utility points that's better then the system that always give me 7 utility points.
However, it seems to me that the situation is much more along the lines that an honest approval vote gives me 2 utility points, and a strategic one gives me a utility of 9.
See, I hold to political positions that almost always put me in the minority. If I only approved those candidates that that I actually liked, I'd only approve candidates with effectively zero chance of winning. This would let my least favorite candidate win, thus granting me very little utility.
Hence, I'll probably take System X, even if approval voting might, in theory, do better if everyone applied the strategy correctly.
