Does it solve the problem of human nature? NO.....and no system can or ever will, so criticizing it because "human nature" makes it fallible isn't a very strong argument due to the fact all systems are subject to this "human nature". Basically the "human nature" argument is irrelevant due to the fact all systems of governing will face the same such said "human nature"
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You are quite wrong. Human Nature is exactly why Libertarianism never works.
If the majority of a people decide they want a welfare program, would a Libertarian government block it? You must. If you don't, you quickly no longer have a Libertarian system.
But restricting and blocking such initiatives by the people would be fascist, would it not?