  Suppose one adds to the desert principle the further norm that when a person has less than she deserves, it is morally more valuable to gain an increment of good fortune for that person, the greater the gap between what she has and what she deserves. Call the further norm the greater gap principle. Just as the prioritarian regards it as morally more valuable (a matter of greater moral urgency) to gain a benefit for a person, the worse off in absolute terms she would otherwise be, the greater-gap desertitarian as just characterized holds that it is morally more valuable (a matter of greater moral urgency) to gain a benefit for a person, the greater the shortfall (if any) between the benefit level she has and the benefit level she deserves. Accepting the desert principle and the greater gap principle, one will then sometimes favor egalitarian transfers purely from considerations of desert.