 This concept can also be related to the idea of equality of opportunities (Kolm 1996). An allocation is envy-free if and only if the bundles granted to everyone could have been chosen by each individual in the same opportunity set, such as, for instance, the set containing all the bundles of the allocation under consideration. Along this vein, the concept of no-envy can also be shown to have a close connection with incentive considerations. A no-envy test is used in the theory of optimal taxation in order to make sure that no one would have interest to lie about one’s preferences (Boadway and Keen 2000). Consider the condition that, when an allocation is selected and some individuals’ preferences change so that their bundle goes up in their own preference ranking, then the selected allocation is still acceptable. A particular version of this condition plays a central role in the theory of incentives, under the name of Maskin monotonicity (see e.g. Jackson 2001), but it can also be given an ethical meaning, in terms of neutrality with respect to changes in preferences. Notice that envy-free allocations satisfy this condition, since after such a change of preferences every individual’s bundle goes up in his ranking, thereby precluding any appearance of envy. Conversely, it turns out that this condition implies that the selected allocation must be envy-free, under the additional assumption that, in any selected allocation, individuals with identical preferences must have equivalent bundles. If one also requires the selection to be Pareto-efficient, then one obtains a characterization of the competitive equilibrium with equal shares (Gevers 1986).