 To see why not, consider whether it would be socially preferable, starting from the status quo \(S\), to take one apple and one orange from Bob and give both of them to Ann. Let \(T\) be the state arising from this transfer. We assume for the sake of the example that Ann always strictly prefers having more of everything for herself to having less, and that Bob’s preferences are similarly self-interested, so that in all admissible profiles Ann strictly prefers \(T\) to \(S\), while Bob strictly prefers \(S\) to \(T\). Their preferences among these states are opposite and do not by themselves entail a social preference one way or the other. Now, consider first a profile in which the status quo \(S\) is envy free but \(T\) is not. (Let both Ann and Bob be indifferent between the baskets each one has in \(S\) but not between those in \(T\), in which both agree that Bob is worse off.) Relative to this profile, a social welfare function promoting envy freeness comes out against the transfer from Bob to Ann by ranking \(S\) strictly above \(T\). But consider another profile, in which it is \(T\) that is envy free (now Ann and Bob are indifferent between the baskets in \(T\), and agree that in \(S\) Ann is worse off than Bob). Relative to this second profile, \(T\) outranks \(S\) in the social ordering. In direct conflict with I, the social preference among \(S\) and \(T\) switches as we go from one profile to the other, although the individual preferences among \(S\) and \(T\) stay the same. The social ranking of \(S\) and \(T\) turns on preferences among these states and the “irrelevant” \(S^*\) and similarly defined \(T^*\), because the fairness of \(S\) and \(T\) does.