Preserving Dominance Relations Through Disaggregation: The Evil and the Saint

This paper investigates the circumstances in which stochastic dominance relations at any finite degree at the household level can be assumed to be preserved at the individual level. We find necessary and sufficient conditions on the common sharing function adopted by households to divide the cake among a "strong" and a "weak" individual. The sharing function which maps the household income into the outcome of the weak individual must belong to the class of utility functions which supports the stochastic order. In addition, the household must follow a compensating rule, meaning that the share of resources devoted to the weak individual increases with household income. Applications to fiscal federalism are also proposed.