The 'unconditional' I take to mean that everyone, rich and poor, would get the same money. So even though the people with high income are paying more in taxes to cover this, they're also getting the same amount paid to them in a separate check. So yes, they're paying more in taxes, but they're also getting the same benefit as everyone else, and this will take some of the sting off.
UBI is an excellent libertarian/small-government solution.
UBI is an excellent libertarian/small-government solution.