Sure, democracy that works by majority (or majority party) or whatever makes sense for actual government. But my street is not a government, and devolving the sort of power to change rules and impose fines, liens or whatever on my house to the rest of the folks in the street, without even requiring unanimous agreement on the rules by all the property owners, is just nuts.
I would never put myself at the mercy of whoever I happen to live on a street with like that. I'm glad these things are rare to non-existent in the UK.
I don't think that democracy is not synonymous with a 51% majority. There's super-majorities, consensus, and unanimous votes.
A lot of people who strongly believe in democracy (real democracy) don't believe that 51% of the people should be allowed to impose their views on the other 49%. That can lead to big problems. They would say to keep talking, negotiating, and compromising, and that it you can't reach consensus then the proposal should not be passed.
Well, indeed it seems almost impossible to get a good "rules of democracy", but if the majority wants something and they don't get it, that's the tyranny of the minority, that kind of defeats the purpose of democracy. (It's easy to say that passing new motions/resolutions/laws require consensus, but if the current system benefits a minority that can block the new laws ... you have a problem.)
Obviously, on the other hand if 50% + 1 can do whatever just happens to be on their mind, that seems like a very-very bad (or good, if you are the more evil-er sibling to Satan) recipe for disaster.
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And here were are. Extreme polarization, fight for survival, everything is up for grabs (voting rights, citizenship/deportation, budget, supreme court seats, filibuster).
Justice is hard. (Rawls' Theory of Justice proposes that what's fair is just, and it defines that as a reflective equilibrium ... which seems a pretty elegant solution - especially if you have spent too much time in abstract math classes.)
If a group of people can't reach consensus then the ideal may be to split into smaller groups, not force minorities to conform?
Nothing an HOA does is an emergency. Even if 2/3 of the people want to change the rules for parking, for example, they shouldn't get to screw over the people who bought the place without that rule and are vehemently opposed to such a change.
Scaled up to country size, like you mentioned, trying to get 330 million people to agree how the federal government allocates 25% of our national GDP turns out to be a big mess, especially when the slim majorities in congress change back and forth every handful of years. Maybe that's why the tenth amendment was put in place.
There are shared/common resources. Environment (air, water, wildlife, etc.) There are stuff that cannot really be solved locally. Simply waiting and trying to persuade each other is very civil, but it has a cost. (Yes, it's very-very-very likely smaller than trying to usurp control with violence, but not every region/country is as fortunate as the US.)