It's an interactively generated thing, so the govt can ensure you can only complete it once, while being ignorant of its content. Or at least that's the claim of these protocols (e.g. Camenisch–Lysyanskaya (CL) signatures) afaik. I'm not sure how they work in detail.
Why, though? If you're the only one who knows it, nothing prevents you from creating as many identities for the same site as you wish.