The Pigou-Dalton Principle and the Structure of Distributive Justice

The Pigou-Dalton (PD) principle, 1 applied to some type of good, recommends a nonleaky, non-rank-switching transfer from someone with more of the good to someone with less, as long as no one else‘s holdings are changed— non-leaky in the sense that the one who starts out with less of the good gains by exactly as much as the other loses; non-rank-switching in the sense that the one who starts out with less does not end up with more than the other. Here is a formal statement of this principle: Let g = (g1, g2, ..., gN) be a list of the holdings of good G among the population of N individuals, with gi a number quantifying the holdings of any given individual i, and g*= (g1*, g2*, ..., gN*) another such list. If there exist two individuals h and l such that gh > gl, ∆ > 0, gh* = gh − ∆ ≥ gl* = gl + ∆, with gi = gi* for every other individual i in the population, then g* is an improvement over g.