The Modigliani Miller Theorem says that a firm's financing policy is irrelevant. It's wrong of course, but it's a good place to start thinking about firms' financing policies.
It would be presumptuous to talk about an Irrelevance "Theorem" for Basic Income. The math is trivial, and the economics is obvious. (And I hope this is not at all original.) But it might be an equally good place to start thinking about Basic Income.
There is only one assumption needed for the Irrelevance "Theorem": the only thing that matters to individuals and to the government is Net taxes (taxes minus transfer payments).
Let there be an initial net tax function Ni = N(Income of individual i, other stuff). It is possible to define a new net tax function M( ) - C = N( ), where C is some constant. Interpret C as "Universal Basic Income". Done. An outside observer, who observed only the net taxes each individual paid, would be unable to distinguish between a system with and without a Universal Basic Income.
If we want to argue for or against UBI, we must argue that the assumption is false. For example:
- Framing Matters. It makes a difference to individual behaviour whether they frame a (say) 50% marginal net tax rate as a 50% clawback of welfare or as a 50% income tax with no clawback. Since the presumably educated chattering classes often can't see through the framing (or I wouldn't need to write this post), this is not implausible.
- Taxes are an individual obligation and government right, and transfer payments are an individual right and government obligation. If the default option is that neither government nor individual pays the other anything, it might make a difference who has the obligation and who has the right to do what. Sort of like where the Coase Theorem doesn't work because of "transactions costs".