Applying your statement above: If THE PEOPLE are charged with determining who gets to use the land, and if that charge must be executed under the real premise that THE PEOPLE all have equal right to the land, how do THE PEOPLE arrive at a determination that my neighbor shall have a 10,000 acre ranch and I shall have a 1,000 sq ft apartment on the 5th floor of an apartment building?
They create a government entity to make that decision based on the ethical standards the people choose to adhere to. It's a called 'representative government'.
Again, how is it arrived at that my neighbor's necessity equals 10,000 acres while my necessity equals 1,000 sq ft?
There are many factors involved that are unique to each society.
By what standard do THE PEOPLE come to this determination?
Not by what "standard", but by mutual agreement. When their government no longer represents their collective needs or desires sufficiently, they will do away with it and create a new one.
Also, how does that interference maintain peace? How does that interference maintain equilibrium?
By force if necessary. But mostly by mutual agreement.
It's only in the last 4 decades that the American people have become so childish and so selfish that they can no longer tolerate any form of government oversight or interference. Before then, most people understood that their government represented the well being of the society as whole, and that even though this might contradict the well being of some individuals within the whole, those individuals must recognize that the needs of the many outweigh the needs of the one, or of the few. And that although the government is never going to be perfect, it is nevertheless, necessary, and is trying to do it's job.
But as the government has become more and more corrupted by the massive wealth of a small group of elites (created by capitalism) it has become less and less representational of anyone else. And the people have lost their trust in it. So now they think only of themselves, and resent any sort of government interference.