111 research outputs found

### Single Crossing Lorenz Curves and Inequality Comparisons

Since the order generated by the Lorenz criterion is partial, it is a natural question to wonder how to extend this order. Most of the literature that is concerned with that question focuses on local changes in the income distribution. We follow a different approach, and define uniform $\alpha$-spreads, which are global changes in the income distribution. We give necessary and sufficient conditions for an Expected Utility or Rank-Dependent Expected Utility maximizer to respect the principle of transfers and to be favorable to uniform $\alpha$-spreads. Finally, we apply these results to inequality indices.Inequality measures, Intersecting Lorenz Curves, Spreads

### The ignorant observer

We propose an extension of Harsanyi's Impartial Observer Theorem based on the representation of ignorance as the set of all possible probability distributions over individuals. We obtain a characterization of the observer's preferences that, under our most restrictive conditions, is a convex combination of Harsanyi's utilitarian and Rawls' egalitarian criteria. This representation is ethically meaningful, in the sense that individuals' utilities are cardinally measurable and fully comparable. This allows us to conclude that the impartiality requirement cannot be used to decide between Rawls' and Harsanyi's positions.Impartiality, Justice, Utilitarianism, Egalitarianism, Decision under ignorance.

### Measuring Inequalities without Linearity in Envy Through Choquet Integral with Symmetric Capacities

International audienceThe (generalized) Gini indices rely on the social welfare function of a decision maker who behaves in accordance with Yaari's model, with a function f that transforms frequencies. This SWF can also be represented as the weighted sum of the welfare of all the possible coalitions in the society, where the welfare of a coalition is defined as the income of the worst-off member of that coalition. We provide a set of axioms (Ak) and prove that the three following statements are equivalent: (i) the decision maker respects (Ak); (ii) f is a polynomial of degree k; (iii) the weight of all coalitions withmore than k members is equal to zero

### Fairness under Uncertainty

Ever since its introduction by Foley (1967) and Varian (1974), the notion of fairness has been one of the most extensively used notion to evaluate allocations on an ethical basis. Whereas thereis an extensive literature on the efficiency properties of allocations in economies with uncertainty the concept of an envy-free allocation has not been widely studied in economies with uncertainty. We introduce two very natural notions of equity in an economy under uncertainty, namely ex ante and ex post equity, show they can contradict efficiency requirements. In particular, the set of ex ante efficient and ex post envy-free allocations may be empty. We nevertheless show that, under special circumstances, one may prove the existence of allocations that are both ex ante efficient and ex post envy-free. Such is the case, in particular, in an economy with individual risk and no aggregate risk.

### Beliefs and Pareto Efficient Sets: A Remark

We show that, in a two-period economy with uncertainty in the second period, if an allocation is Pareto optimal for a given set of beliefs and remains optimal when these beliefs are changed, then the set of optimal allocations of the two economies must actually coincide. We identify equivalence classes of beliefs giving rise to the same set of Pareto optimal allocations.Beliefs, Pareto Optimality

### Fairness under Uncertainty

Ever since its introduction by Foley [1967] and Varian [1974], the notion of fairness has been one of the most extensively used notion to evaluate allocations on an ethical basis. Whereas there is an extensive literature on the efficiency properties of allocations in economies with uncertainty the concept of an envy-free allocation has not been widely studied in economies with uncertainty. We introduce two very natural notions of equity in an economy under uncertainty, namely ex ante and ex post equity, show they can contradict efficiency requirements. In particular, the set of ex ante efficient and ex post envy-free allocations may be empty. We nevertheless show that, under special circumstances, one may prove the existence of allocations that are both ex ante efficient and ex post envy-free. Such is the case, in particular, in an economy with individual risk and no aggregate risk.Fairness, uncerainty, envy

### Multidimensional generalized Gini indices.

The axioms used to characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered.Generalized Gini; multidimensional inequality

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