In my opinion, democracy exists because it greatly lowers the cost of legitimizing government. Governments can exist because the cost of threatening coercion is less than what people are willing to pay to be free from coercion (i.e., taxation). A legitimized government will be able to tax far more easily than a despotic one, and so it will generate more profit. This increase in profit means that democratic forms of government will tend to expand and consume other less efficient forms of governance, just like a more profitable firm replaces its competitors. Convincing the taxed and regulated populace that you're there to serve them is a lot cheaper than ruling with brute force, after all.
I'd say normative arguments in favor of democracy aid in its adoption not because people strive to do what is 'right', but because those normative arguments create an opportunity for political entrepreneurship. So I think they are something of a tautology: If we can convince people democracy is good for them, democracy will succeed.