David Elkins (SMU) has published Horizontal Equity as a Principle of Tax Theory, 24 Yale L. & Pol’y Rev. 43 (2006).  Here is the abstract:

The principle of horizontal equity is usually accepted on intuitive grounds. Whereas the other major principles of tax theory – vertical equity and economic efficiency – have been the subject of vast literature, the theoretical underpinnings of horizontal equity are rarely if ever challenged. The question raised by this article is whether horizontal equity has a theoretical basis and, if so, what that basis is.

The article first considers the possibility of deriving horizontal equity from economic efficiency, from vertical equity and from the principle of equal protection or equality before the law. None of these, however, proves successful.

A deeper analysis of horizontal equity shows that it is fundamentally an anti-redistributionary principle. This would seem to indicate that the normative basis of horizontal equity should perhaps be sought within the framework of social theories which attach moral justification to the market distribution. The problem here is that those theories tend to undermine the State’s moral authority to lay taxes in the first place. The article therefore examines attempts by social philosophers to design a tax structure which recognizes as inviolable the moral obligation to respect the market distribution, and the place of horizontal equity therein.

The conclusion reached is that horizontal equity cannot at present be normatively justified. However, anticipating possible future developments in social philosophy, a more moderate conclusion would be that any normative grounding of horizontal equity would be in direct conflict with that of vertical equity.