Abstract
This study discusses the characterization of the lexicographic maximin (leximin) choice rule using an axiom related to the Lorenz criterion, which states that a utility vector that Lorentz dominates a solution vector should not be Pareto dominated by any feasible vector, named Pareto Undominatedness of Lorenz-superior Distribution (PULSD). PULSD in itself does not imply that a solution vector of the choice rule is Lorenz undominated by any utility vectors in the feasible set. Therefore, we may say that the PULSD’s requirement for inequality aversion is weak. Indeed, PULSD is consistent with the utilitarian choice rule, which is viewed as indifferent to equity. We show that the leximin choice rule is characterized by PULSD, combined with the Suppes-Sen optimality and the common ordinal invariance axiom.
Highlights
We consider a choice problem to select the optimal distribution from a set of feasible alternatives that represent utility vectors
This study discusses the characterization of the lexicographic maximin choice rule using an axiom related to the Lorenz criterion, which states that a utility vector that Lorentz dominates a solution vector should not be Pareto dominated by any feasible vector, named Pareto Undominatedness of Lorenz-superior Distribution (PULSD)
PULSD in itself does not imply that a solution vector of the choice rule is Lorenz undominated by any utility vectors in the feasible set
Summary
We consider a choice problem to select the optimal distribution from a set of feasible alternatives that represent utility vectors. SSO requires that a solution utility vector be not Suppes-Sen dominated by any utility vector s in the feasible set. A solution vector may be required to be Lorenz undominated by any utility vectors in the feasible set, which we refer to as Lorenz undominatedness (LU). LPO requires that a solution be neither Pareto dominated nor Lorenz dominated by any vector in the feasible set. The leximin choice rule may be characterized without directly requiring a solution vector to be Lorenz undominated by any vector in the feasible set. Instead of LU, LPO, or GLO, we use the axiom, what we refer to as Pareto undominatedness of Lorenz-superior distribution (PULSD), which requires that a feasible or infeasible utility vector that Lorentz dominates a solution vector be Pareto undominated by any vector in the feasible set.
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