Define 'bind', please.
If my neighbourhood elects representatives who decide that we should all have black trash bins, then how am I 'bound to abide by their decision' if I want to put out a green bin instead?
The problem is moot if the decision is unanimous, since a unanimous decision has no dissent by definition. It comes back with any rule from authority, even if that authority is republican in nature. Note that I said coercion, which is broader than a simple threat of violence; shame and shunning are some of the oldest coercive tactics in the book.
Majoritarian government is great because it offers an easy path to legitimacy, overcoming the 'who died and made you leader?' problem. However, my argument speaks to the leader part of that question, not the you part.