If I may comment, without participating in the disagreements you have had upthread with other posters, I would like to add: I agree that such an inverse relationship exists however I would say it's not necessarily a causal relationship. It could be merely correlative in nature (which as at least some know doesn't prove much).
Consider that the very heart of tyranny as seen in places like NYC is due to the very (fallen) nature of man. He seeks to control his environment around him by default. Sometimes to the detriment of his fellow man. Indeed this is fundamentally due to a lack of faith in Another to whom we belong. Man naturally has a desire for the infinite, infinite beauty infinite Justice. However when this is not realized via Faith in Christ, corruption of the infinite desire for Him is the inevitable result. This corruption can and does take many forms, one of which is a concerted effort by some to reach into and seek control of the lives of others. All in the name of "Justice" (but of course is nothing of the sort. It's tyranny not Justice.
So to conclude in brief: the problem of diminishing Liberty is not caused by "overpopulation" (whatever that means anyway). Diminishing liberties are made manifest more easily in population centers, because it is easier to "justify" them there. But greater populations aren't the cause per se. It's caused by men fundamentally not recognizing who and what they are, which are creatures of God made for Him, to serve Himmand his fellow man. So the decrease in liberties in population centers won't be solved by means of population growth controls. They will really wont be solved until and unless man comes to know his true nature and destiny, who is Jesus Christ.
In the event, of course, the South did not prevail but I believe the truth of the statement does. Someone else said we should work as though the entire responsibility were ours and pray as though everything were in God's hands. I take this to mean that in the political sphere we have our jobs to do and we cannot heap all responsibility on God.
Equally (and that means, equally) our political condition ultimately depends on our spiritual condition. If we have a constitutional republic that cannot succeed according to John Adams unless we have a virtuous people, I say we cannot have a virtuous people without the fear of God.
We can argue chicken and egg, whether virtue can survive in a densely populated area or whether vice causes densely populated sewers but we have our half of the job that cannot be ignored. We should not invite the vice of overpopulation and then expect God to redeem us.