The basic design is simple. You give every person a single dollar amount as a MBI and then ALL income (besides the MBI) is taxed at a flat rate of X percent. For example (and just using simple numbers for maths sake) pretend that the MBI is $10,000 and the tax rate is 10%. Everyone making LESS than $100,000 would actually receive a subsidy because their overall paid tax would be less than the $10,000 they received from the MBI. Everyone over $100,000 would pay a progressively higher tax approaching 20%. The results are:
1) A tax rate that is perfectly progressive providing a MBI and fully scaled real tax rate for everyone. 2) Increased income has no tax disincentives (your tax rate doesn't change because you move into a higher income.) 3) Simplifies that tax code dramatically (which would also increase revenue.) 4) Doesn't artificially encourage capital gains manipulation by large income holders. 5) Removes government manipulation of social policy by giving them ONLY two number to play with... MBI and tax rate! 6) Finally, it provides a real mechanism for everybody to feel the effects of tax rate changes. Making it MORE responsive to economic factors like income inequality. For example, if 90% of people would get more money in their pocket by increasing the MBI to $15,000 while also increasing the tax rate to 30%... the likelihood of that change actually passing through Congress is dramatically higher that it currently is because such a system is transparent to your own pocketbook.
ALL of these effects without negatively affecting market freedom. Again, we see Libertarian thought is both MORE "fair" AND more compassionate.