Libertarian Thought Experiment

Imagine if you will, that libertarians have taken over a state and seceded from the United States.  Libertarians ideals are fully implemented. There is no minimum wage for example, and libertarians from the rest of the United States have migrated there.  How long would this last?

I ask this because libertarians are among those on the right who call for open borders.  The practical effect of an initially successful libertarian state would be an initial economic success that would attract those without skills to work at wages that are illegal in the U.S.  How long before the libertarian businessmen of Libertopia were making fat profits selling goods produced with low cost labor back into the U.S.? How long before Libertopia is overrun with migrants from cultures who don't value limited government?  How long before they have the votes to end libertarianism and vote themselves minimum wage hikes, benefits and extended unemployment benefits?

The fact is that generally, throughout history, only a few cultures have been in favor of limited government with separation of powers, such as the United States has had.  Further, those cultures have concentrated in Europe.  There is good evidence that some of this predisposition is heritable. Unlimited immigration from the Middle East, Africa and Latin America means bringing voters to America who don't value limited government and separation of powers as well as other rights, like freedom of speech.  Those of us who support a political system inherited from England will get out-voted by increased immigration.

The conundrum for my libertarian friends is that strict libertarianism destroys libertarian society.