Preserving Dominance Relations Through Disaggregation: The Evil and the Saint
Disaggregation arises when broad categories like households budget units are divided into elementary units as individual income recipients. We study the preservation of stochastic dominance for every order beyond two after disaggregation: If we observe a dominance relation among household income distributions, it is also true at the individual level. We find necessary and sufficient conditions satisfied by the common sharing rule adopted by households to divide the cake among individuals. The sharing function, which maps the household income into the outcome of the disadvantaged individual, must have derivatives of the same sign as the utility function characterizing the stochastic order of interest. In addition, the household has to follow a compensating rule, meaning that at the margin the distribution should be in favor of the disadvantaged individual.
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