On Dividing an Amount According to Individual Claims or Liabilities

A basic principle of distributive justice states that if an allocation among a group of individuals is fair, then it should be perceived as fair when restricted to each subgroup of individuals. This ‘consistency’ principle applies in particular to methods for allocating taxes among citizens according to their ability to pay. Every consistent, continuous taxation method optimizes an additively separable objective function. Optimal allocations may be computed by a simple Lagrange multiplier technique. Similar results hold for allocating assets among creditors according to their claims. The techniques are illustrated by constructing an objective function for a bankruptcy method from the Babylonian Talmud.