 The theory of fair allocations contains many positive results about the existence of fair allocations, for various fairness concepts, and this stands in contrast to Arrow’s impossibility theorem in the theory of social choice. The difference between the two theories has often been interpreted as due to the fact that they perform different exercises (Sen 1986, Moulin and Thomson 1997). The theory of social choice, it is said, seeks a ranking of all options, while the theory of fair allocation focuses on the selection of a subset of allocations. This explanation is not convincing, since selecting a subset of fair allocations is formally equivalent to defining a full-blown albeit coarse ranking, with “good” and “bad” allocations. A more convincing explanation lies in the fact that the information used in fairness criteria is richer than allowed by Arrow’s Independence of Irrelevant Alternatives (Fleurbaey, Suzumura and Tadenuma 2002). For instance, in order to check that an allocation is envy-free while another displays envy, it is not enough to know how individuals rank these two allocations in their preferences. One must know individual preferences over other alternatives involving permutations of bundles (an envious individual would prefer an allocation in which his bundle is permuted with one he envies). In this vein, one discovers that it is possible to extend the theory of fair allocation so as to construct fine-grained rankings of all allocations. This is very useful for the discussion of public policies in “second-best” settings, that is, in settings where incentive constraints make it impossible to reach Pareto-efficiency. With this extension, the theory of fair allocation can be connected to the theory of optimal taxation (Maniquet 2007), and becomes even more relevant to the political philosophy of redistributive institutions (Fleurbaey 2007). It turns out that the egalitarian-equivalence approach is very convenient for the definition of fine-grained orderings of allocations, which provides an additional argument in its favor. A detailed study of fair social orderings is made in Fleurbaey and Maniquet (2011b).