A central strand in philosophical debate over the just distribution of resources attempts to juggle three competing imperatives: helping those who are worst off, helping those who will benefit the most, and then – beyond this – determining when to aggregate such ‘worst off’ and ‘benefit’ claims, and when instead to treat no such claim as greater than that which any individual by herself can exert. Yet as various philosophers have observed, ‘we have no satisfactory theoretical characterization’ as to how (...) to weigh each of the three imperatives against one another, we find it ‘difficult to state... precise or comprehensive conclusions’, and we do not yet have a ‘metric for integrating the three measures’. In what follows, I offer an approach to weighing the three criteria against one another that yields resolutions – in Hard Cases of the ‘saving one infant's life versus replacing ten elderly people's hips’ sort – that are cardinally definitive, intuitively satisfactory and theoretically justified. (shrink)