Non-proportional inequality preservation in gains and losses
Abstract We characterize the family of claims-inequality and claims-order preserving continuous rules in the three-agent case for the problem of adjudicating conflicting claims. We show that there are infinitely many of such rules and provide a simple geometric construction that spans the whole family. Additionally, we prove that this family endowed with the partial order of Lorenz domination is a lattice that has maximal and minimal elements.
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