Relativism and Democracy

I am struck by this passage from Tocqueville: “I have previously stated that the principle of the sovereignty of the people hovers over the whole political system of the Anglo-Americans. Every page of this book will reflect certain fresh instances of this doctrine. In nations were it exists, every individual takes an equal share in sovereign power and participates equally in the government of the state. Thus he is considered as enlightened, virtuous, strong as any of his fellow men.” Toqueville’s point is that democracy presupposes that each person is as competent and virtuous as any other. But of course this is false: people differ widely in intelligence and virtue. Note that he says “considered” not “really”. So democracy rests on a lie. How, then, to defend democracy? Well, if truth, reason, virtue, etc are not objective qualities that people exemplify to varying degrees, but are rather relative to each person, we have a way out: everyone is as smart and good as anyone else to himself. Then democracy rests on no lie, since everyone really is cognitively and morally equal. Relativism steps in to save democracy from its noble lie. Thus relativism finds a foothold. But relativism is rubbish; so where does that leave democracy?