Rationalizing formula apportionment

Many federal tax systems employ formula apportionment to allocate the taxable profits of large businesses to the federal subunits, where the subunits' specific tax rates are then applied. The formulas - such as the one recently proposed by the EU Commission and the one agreed upon by the OECD/G20 Inclusive Framework - are remarkably similar, yet their underlying rationale, particularly the normative criteria from which they are derived, remains largely unexplored. To address this gap, I adopt an axiomatic approach and derive a generalized system of formula apportionment based on three criteria: fixed coverage, positive responsiveness, and external independence. I demonstrate that any formula apportionment system meeting these three criteria will suffer from the same distortion, unless all local tax rates are identical. The generalized system encompasses existing real-world systems, as seen in federations like the US, Canada, and Germany, as special cases, while offering a degree of flexibility that holds the (thus far unrealized) potential for surplus-increasing reforms.