Suppose, for simplicity, that the basis for moral desert is virtue and what’s deserved is well-being. According to the Ratio View of Comparative Desert, for two people to get what they comparatively deserve, the ratio of their levels of well-being must be the same as the ratio of their noncomparatively deserved levels of well-being. That is, if A noncomparatively deserves 10 units of well-being (A’s ‘peak’ is 10) and B noncomparatively deserves 20, they get what they comparatively deserve whenever B gets twice as much as A. So if A’s level is fixed at 15 (there’s no way to change it), B comparatively deserves 30.
This is an appealing view with an impressive pedigree (it is suggested by what Aristotle says about distributive justice, for example). But recently Shelly Kagan (2003, forthcoming) has presented seemingly devastating objections to it. I'll try out a straightforward response to them. It'll require that there is, at least, a lower bound to well-being.
Here’s Kagan's first objection:
But it is not so clear what advocates of the ratio view should say if A’s actual level of well-being is a negative number (a life not worth living). Suppose, for example, that although A’s peak is at 10, we can do nothing about the fact that his level of well-being is at -10. Where should B be placed so as to satisfy comparative desert? Since B is twice as virtuous as A, advocates of the ratio view seem committed to the view that B's level of well-being should be twice that of A’s. But this seems to mean that if A’s level is fixed at -10, the ratio view demands that B be placed at -20! (Kagan 2003, 101)
Kagan notes that this could be fixed by reversing the ratio when we go negative, but this won’t help with two further problems. If A’s peak is at 0, the ratio to B’s peak will be undefined. If A’s peak is negative, say -10, and B’s positive, say 20, the ratio will be a negative unit of well-being for A for two positive units for B. But, Kagan points out, if A’s level is fixed at -5, this tells us that B’s should be at 10. He rightly notes this is unacceptable: it would mean that comparative desert would require B to be worse off than ideal while A is better off than ideal! Kagan takes such cases to constitute a definitive objection:
As far as I can see, there is simply nothing plausible for the advocate of the ratio view to say at this point. I believe that cases like this last one sound the death knell for the ratio view. It simply must be abandoned. (Kagan 2003, 103)
My response to Kagan is so simple-minded that I suspect there must be something wrong with it, but I can’t yet see what it is. (I should also note this isn't a literature I know well at all. Googling hasn't revealed any similar response to Kagan - apologies in advance if this is old hat.) All the problems he raises for the Ratio View result from the fact that the scale he uses to represent well-being goes to zero and below. But as far as I can tell, this is a matter of pure stipulation. After all, any numerical value we give to someone’s level of well-being is just a potentially useful way to represent it for some purpose. There is some intuitive appeal to use negative numbers to represent doing badly (that is, having a low level of well-being), but I can't see why we would be compelled to do so. So why not stipulate otherwise in order to avoid the problems caused by this means of representation for an otherwise appealing view?
Here’s one way to do it. Everyone alive has a level of well-being of at least 1. (The dead don’t have a level of well-being.) 1 is really bad, though – it is a life of unimaginable agony. It’s a life most would prefer to end, a life truly not worth living. It is the lower bound of well-being. It can’t get any worse than that. It’s deserved by Hitler, presumably. Mapping well-being on a positive scale requires that there is lower bound, so I’m making an assumption that Kagan doesn’t have to make. On the other hand, since it is independently plausible, it is itself a reason to represent well-being on some such scale. Of course, we’ll need to pick some number to represent neutrality. Let’s say we use 100 for it. It is the level of well-being deserved by someone neither vicious nor virtuous. If well-being has an upper bound (which I consider a realistic assumption) we can use 1000, say, to represent it. This is strictly optional, but it seems realistic to me, too.
If well-being has bounds, we’ll easily get into situations in which claims of comparative desert can’t met. If A noncomparatively deserves 120 and B noncomparatively deserves 360, but A unalterably enjoys 400 units of well-being, it is impossible for B to get what she comparatively deserves, since it is off the scale. Alas, that’s life. Also, this puts a limit to how much more well-being one person can deserve than another (Mother Teresa can deserve at most 1000 times what Hitler gets), unless we can noncomparatively deserve an impossible level of well-being. That doesn’t seem implausible to me either.
Let’s translate Kagan’s cases to this scale. In the first, the peaks have a 1:2 ratio, and A’s level is fixed at -10 for him. So for us, let’s stipulate A has 80. Great, B comparatively deserves 160. In the second case, A is at his neutral peak. When that is set to 0, it looks like any level for B will satisfy comparative desert. But on my scale, it’ll be 100. If B’s peak is at 120, the 10:12 ratio will only be satisfied if B is at 120. Which is exactly how it should be. In the last case A deserves to do badly and B somewhat well. Let’s stipulate the deserved levels are 80 and 140. Now A is at 90 – he’s doing better than he should. The ratio scale says that B should be at 8:14 ratio, which works out to 157.5. So by comparative desert, she should be doing better than her peak, and the increase should be bigger quantitatively than A’s. That seems all right.
Now, I admit this isn’t as pretty as it could be. But it does seem to avoid the problem Kagan raises, and desert according to it could be graphed on the upper right hand corner of Kagan’s scales. Is the Ratio View better than Kagan’s Y Gap model, on which, roughly speaking, comparative desert is a matter of ‘similar offense’ against noncomparative desert? It’s very hard to say, as the implications of the Y Gap view depend on the shape of the desert curves. One thing in favour of the Ratio View, however, is that it also captures the notion of similar offense, and does so in a way that makes the similarity of the offense depend on the relative peak levels. In any case, if I’m right about the means of representation, we haven’t yet heard the death knell of the Ratio View.