Blockchains are full of coordination games, and they all depend on legitimacy writes Vitalik Buterin:
Legitimacy is a phenomenon that arises naturally in coordination games. If you're not in a coordination game, there's no reason to act according to your expectation of how other people will act, and so legitimacy is not important. But as we have seen, coordination games are everywhere in society, and so legitimacy turns out to be quite important indeed.
You can get legitimacy in a lot of different ways: brute force, process, and participation being three.