Mark Fleurbaey (2007) has shown that social welfare functions need more ordinal information than I allows them if they are to respond appropriately to a certain fairness of social states. He gives the example of Ann, who has ten apples and two oranges, and Bob, with three apples and eleven oranges. This allocation is said to be “envy free” if, intuitively, she is at least as happy with her own basket of fruit as she would be with his and, similarly, he is as happy with his own basket as he would be with hers. Let the distribution of fruit in one social state \(S\) be as described, and consider the state \(S^*\) in which the allocations are reversed. That is, in \(S^*\) it is Ann that has three apples and eleven oranges, while Bob has ten apples and two oranges. More technically, \(S\) is envy free if Ann weakly prefers \(S\) to \(S^*\), and Bob does too. We might expect that, other things being equal, the envy freeness of a social state will promote it in the social ordering above an alternative state that is not envy free. But I does not allow this.