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.

17 Replies to “Comparative Desert and the Bounds of Well-Being

  1. So we are supposing that there are facts both about what one non-comparatively deserves and what one comparatively deserves. And the worry is, I am thinking, that when it comes to comparative desert if one person’s level of well-being is immovable, that will force us to say that comparative desert for the movable person may well be much lower than is intuitive. My first reaction is that this helps show the relative unimportance of comparative desert as opposed to non-comparative desert. But if we are talking about comparative desert and one person’s welfare is stuck at a certain level, then it seems that the thing for comparative desert to say is that the best way to give people what they comparatively deserve is to be quite wide of the mark of what they non-comparatively deserve.

  2. Antii, can you explain (for those of us who have never thought about comparative desert before) what the significance is supposed to be of comparative desert?
    Just speaking personally, I have no intuitions about whether it might turn out that a person who deserves to suffer ‘comparatively deserves’ great riches when someone who deserves riches is suffering (as in the Death Knell cases). I mean, that’s how the thing was defined, and so far I’m not able to see what intuitive concept ‘comparatively deserves’ latches onto.

  3. Hi Antti –
    This is a very interesting post. I’m not sure what to say about the comparative desert idea, and it may be that the plausibility of that kind of thought is enough to outweigh other considerations. But I worry about setting a lower bound to well-being. Take a simplistic case. Imagine a life at 1. Now imagine a slightly longer life, i.e., an extra day of total agony. That seems worse to me. Of course, you might say that welfare scores diminish asymptotically, i.e., there’s a lower limit, and so lives can always get worse. But that also requires us to diminish the marginal disutility of things like days of total agony. But that sounds hard for me to believe, especially if total agony is intrinsically disvaluable. But you might be willing to accept that sort of a view, and if so, fair enough.

  4. Dave, Jamie: A week ago I had never heard the phrase ‘comparative desert’, but it appears to have been a pretty important notion in discussions about desert since Feinberg introduced the distinction. I think its importance is clearest in cases where there is no meaningful measure of noncomparative (or absolute) desert. For example, Tom Hurka argues persuasively that there’s no particular economic reward that people absolutely deserve on the basis of their effort and contribution. But it may still be true that one person deserves a larger share of the total than the other. Insofar as we can make sense of economic desert – I disagree with Hurka on many points, but I think we may be able to make meaningful local comparisons – this seems like an important notion.
    Kagan and others, such as Fred Feldman, assume that in the case of moral desert, there is some noncomparative fact of the matter about how much happiness or well-being someone deserves. I’m agnostic about that myself. But let’s assume that there’s such a thing, and that we have a world with two characters, Sid Vicious and Nancy Neutral. Sid, say, absolutely deserves a low level of well-being, while Nancy deserves a a neutral level of well-being. But alas, Sid, who works for Goldman Sachs, is quite happy in his gilded mansion. The thought is that there’s something good about Nancy being better off (for the Ratio View, proportionately better off) than Sid, although that requires her to be better off than she noncomparatively deserves to be. The world in which she’s better off than Sid is in one respect morally better than the world in which she is neutral. Does this make sense?
    Dale: I thought about the asymptotic model after sending the post. It’s hard to know what to think of an infinity of agony. It could be that the marginal disutility diminishes. (I suppose I’ll find out after I’ve spent infinity in hell – I’ll text the answer to you in heaven.) Alternatively, I could say that my model only works for mortals, or, better, for agents who don’t noncomparatively deserve an infinity of agony. That seems like a fairly chewy bullet.

  5. Hi Antti,
    A follow up on your response to Jamie – I am trying to get into the view too.
    Does the comparative view only tell in favor of upping the better person’s happiness, or does it also commend downgrading the less good person’s happiness?
    For example I am morally decent, but no saint, while Jamie is a moral paragon. I am just as happy as is absolutely fit (I am reasonably happy but stressed and suffer from white man’s guilt), but poor Jamie is only as happy as I am; his saintly self absolutely deserves more.
    Now is the comparative view that it would be a good thing if I became more depressed, thereby ensuring a better ratio? Or maybe: it would be a good making feature of that world, even if that goodness is swamped by my no longer having the absolutely fit amount of happiness?
    Or am I misunderstanding?

  6. Brad, yes, the Ratio View in its simplest form does require an analogue of leveling down. There’s a pro tanto desert-based reason for you to do worse than you do, even though you do just as well as you deserve. Any plausible overall theory of desert would require noncomparative desert to take priority in such a case, I think.
    Still, I can see the intuitive appeal. Imagine that Saint Jamie (clearly no relation to any PEA Soup contributor) is actually unhappy. We might well think there’s something wrong with the fact that you who are morally much worse are doing so much better – that in one respect it would be better if you were doing worse than him rather than better. (This is, of course, more plausible if you believe that virtue deserves to be rewarded by well-being, which I’m not so sure of myself. I’m just playing along.)

  7. Hi Antti,
    I share Dale’s worries. You’ll also need an upper bound of evil. You have to say that the lower bound of well-being is deserved by the worst possible person. If you didn’t say that, then the person who was just a bit worse than Hitler (killed one more person, made one more nasty remark) would deserve a worse life than 1. But, you cannot say that because there is going to the negative. So, you must take there to be a limit to evilness as well. That seems fairly implausible. It seems like you can always be a worse person.
    I’ve got various issues with Kagan’s objection itself but I need to think about it more.

  8. Thanks, Jussi. A brief comment: I don’t need a limit to evil per se, but a limit to how badly off one can deserve to be. It doesn’t seem implausible to me that such a limit could be reached. Let’s say that Satan’s deserts mark the point beyond which you can’t deserve anything worse. To make this even somewhat intuitive (and really, we’re all just fooling around here), suppose that Satan somehow resurrects anyone who ever lived and tortures them, along with everyone living now and everyone who will ever live, in the most extreme and disrespectful way possible, until the end of time. Including their pets. And he enjoys it as much as it’s possible to enjoy anything. He deserves the worst fate possible. So now take Satan+. He’s just like Satan, but he also tortures Satan himself. Now, it’s not clear to me if Satan+ is actually more evil than Satan, but at least he does more harm. (Albeit to a deserving creature. This is a bit of a complication – but what other way could there be for Satan+ to be more evil than Satan?) So let’s stipulate that he’s worse than Satan. (If all it takes is torturing Satan, we’re off to an infinite chain of more and more evil possible creatures.)
    Now, it doesn’t seem obvious to me that Satan+ deserves a worse fate than Satan, if we’ve done our job of imagining Satan (and his just punishment) well enough. Marginal differences in evil need not translate to differences in desert. That is, fairly obviously, our actual practice. We don’t care if Ratko Mladic ordered the killing of 6999 or 7000 Bosnian civilians.
    Alternatively, though my imagination is at its limits when imagining worse possible creatures than Satan, I could easily be convinced that the marginal contribution of additional things left to do for them to their sheer evilness asymptotically approaches zero. Which is all I need, even if any increase in evil requires an increase in deserved ill-being.
    Suppose you buy none of this. In the worst case scenario, I’d have to limit the ambition of the theory to human deserts, since human beings surely can’t be infinitely evil (or good). I wouldn’t lose sleep if the Ratio View didn’t apply to Satan (or worse), at the end of the day. Note that Kagan’s counterexamples don’t rely on extreme evil or virtue either – he’s engaged in a project of finding a rationale and principles for a part of actual moral practice.

  9. Hold on. Isn’t there a problem here with aggregation? How will your view deal with summing up the life-time well-being from the amount of well-being in the parts of the lives? For a period of life that’s not worth living, you need to always give some positive value. For the sake of simplicity, I’m just going to consider years. Consider one short life of one year that was not worth living. You need to give this one year life a positive number of well-being – say 20.
    Now, consider a second life that is exactly twice as long as the first one, ie., two years, and in which the each one of the year’s is identical to the year of the first life. Intuitively, both of the year’s of this life get assigned the value 20 of well-being. How much well-being is there in this longer life? Intuitively 20+20 which is 40. But, on your view, the higher the value, the better the life. So, this means that, on your view, the longer the life not worth living the better it is. That’s got to be wrong. Intuitively the longer life not worth living has to be worse than the shorter one. So, you need to assign a smaller value for it, say 10. But, then, how do you get this smaller number as an aggregate of the values of the one year parts whose values were 20 each?
    The point is that aggregation works well if zero is chosen to represent the neutral life as John Broome does. Your proposal needs to give some completely different account of all of this. I guess you could go wholly holistic but that would be a cost.

  10. Jussi, presumably the deserved levels of well-being are lifetime values in any case. (I think that’s the standard line anyway.) So I don’t think aggregation is going to be a worry. I agree that it would be, for the reason you mention.

  11. Jussi, that doesn’t seem to me to be a huge problem. Just use Celsius when you want to aggregate, but Kelvin when you are looking for the ratios for comparative desert.
    In general to have a ratio scale, you have to have an absolute zero (that than which nothing lower can be conceived), whereas the zero of the neutral level is hardly going to be absolute.
    But I suggest that the lower bound should be represented by zero, not one — you can also assume that there is no possible life with a welfare this low, but that horrible lives can get arbitrarily close. (This eliminates the restriction on how much more good one person can deserve than another.)

  12. Hi Antti – and Jamie,
    point taken about Satan and Satan+. That is helpful.
    With the aggregation, I’m not so sure. Jamie might be right that it’s not a huge problem, but it seems to me that it would be an advantage of the view if you could use the same scale of well-being for both comparative desert and aggregation. The reason for this is that I suspect that there will be cases where we’ll need to do both. You might have a person who is virtuous for the most of his life but vicious for the last year of her life. One view would be that she deserves slightly less well-being for the whole of her life. Another, perhaps more plausible view, would be that she deserves a fair amount of well-being for most of her life and then low level of well-being for the last year. If we want to be able to say the latter kind of things, then we quickly get to aggregation.
    If we need to have an absolute zero point for ratio scales – and I presume that you are right about this, then wouldn’t that be a knock-down argument against the traditional ratio view of comparative desert that is being discussed. It does have a meaningful zero but not an absolute one, and it is making claims about ratios between the points on the scale.

  13. Thanks, Jamie! Funnily enough, I had already made just those changes in the hopes of sending a version of the argument somewhere as a discussion note. Alas, now I’m not so sure (see below).
    Jussi: The whole discussion presupposes that there is some way of assigning deserved lifetime well-being levels according to virtue. That’s a pretty formidable task; if we’re able to do that, we’re probably able to distribute that well-being over the person’s lifetime. For that purpose, say for determining the deserved well-being level for that virtuous year, we can surely use the positive scale, since we’re not going to aggregate.
    Another question is whether we want that. Maybe it’s OK if you do well when you’re vicious, if you’re going to do badly when you’re virtuous! Your suggestion (call it Temporal Coincidence) is after all not required by the common Christian thought that the pious deserve to go to heaven, and sinners to hell.
    But thinking about the relation between the scales did lead me to a serious problem for the proposal. I’m not sure if I’m going to be able to have a uniform scale where the increase of a unit of well-being has the same significance regardless of where it occurs, whatever positive number represents neutrality. This is easy to see just thinking about Kagan’s first case in some more detail. For him, A noncomparatively deserves 10 and B 20, and A actually has -10. Note that the increase in well-being that A actually needs to get to the neutral level (from 10 to 0) is the same as the difference between A and B’s peaks (10 and 20). I said, okay, let’s stipulate A has 80. But how do I represent what A and B absolutely deserve? Let’s try 120 for A, since that’s as far from neutral as 80. That means B must deserve 240 to keep the ratio. But now the increase in well-being that it takes for the actual A to get to neutral is 20, while the difference between A and B’s peaks is 120. Comparative distance from neutrality doesn’t have the sort of significance you might expect. This is probably because A and B’s peaks (and hence the ratio) are set by reference to the absolute lower bound and not neutrality of well-being.
    This is one of those problems that are either fatal or insignificant. I can’t yet decide which.

  14. I’m not entirely sure I understand the rules of the game here. But:
    1. Jussi, I guess I would say that Kagan’s objection does exploit the fact that the scale he was thinking of has what we might call an “arbitrary zero” rather than an “absolute zero”. (Not that there is no reason to put zero at the neutral level, but that from the point of view of computing ratios there’s no reason to pick that point as zero.)
    2. Antii, I agree that it turns out that comparative distance from the neutral level doesn’t have the significance that Kagan’s opponent seemed to think it had. But that is bound to happen. (This is the big difference between a ratio scale and an interval scale: for a ratio scale, ratios are meaningful, whereas for an interval scale, only ratios of intervals are meaningful, not absolute ratios.)

  15. Hi again
    That objection and what Jamie is saying puts a finger on what worries me about Kagan’s formulation of the objection.
    As far as I can tell, the Ratio View of Comparative Desert makes a simple claim about the correlation of two things: The ratio of the levels of non-comparative desert and the ratio of the comparative deserts. And, that view, does seem to commit you about much else.
    Now, Kagan’s case is such that A’s level of well-being is not what A should non-comparatively deserve. So, I don’t quite understand why a defender of the Ratio view has to say anything about this case and what B should get comparatively. The view does say what B should get if A got what she deserved. But, it doesn’t seem to have to say anything about what B should comparatively deserve when A doesn’t get what she deserves.
    So, the proper objection should be such that A gets what she deserves, we know how much B should get comparatively but it’s indeterminate what non-comparative level B deserves (or something like that). I’m sure that that sort of cases can probably be generated.
    In any case, the non-committal nature of your proposal seemed to be able to do work to avoid the aggregation problem. The idea was that this is just the kind of combined view of well-being and desert that takes no stand on aggregation issues. I wonder if you could take a similar line with your case. You are worried about the distances from A’s undeserved situation to a neutral level of existence and its significance. I’m not sure why a defender of the Ratio view would have to say anything about such things. In the same way as in the aggregate case, maybe differences between absolute levels of well-being (undeserved) and neutral existence are to be measured on some other scale – such as the one that allows aggregation.

  16. For what it’s worth, I don’t think that it’s entirely fair to say that the ratio view has, as Kagan puts it, “Aristotle’s backing”. In EN, when Aristotle writes that what each receives (each person’s share) should be geometrically proportional to that person’s amount or level of some criteria (which can include, but is not limited to, desert), he is referring to distributions of honor, money, “or the other things that fall to be divided among those who have a share in the constitution”. Is well-being one of these things that fall to be divided? Regardless, assuming that it doesn’t make sense to talk of negative shares of something in this context, Aristotle might be supportive of Antti’s idea that the well-being scale bottoms out at “1”.

  17. About comparative desert in general:
    It has played a vital role in real-world arguments about punishment.
    Imagine that the death penalty is applied in a racially discriminatory way, i.e. more often to blacks than to whites even when their crimes are otherwise similar. But imagine further that the discrimination doesn’t impose the death penalty on any blacks who don’t non-comparatively deserve it. It works only by letting whites who do deserve the death penalty off with lighter sentences. (Biased juries just can’t bring themselves to send whites to the gallows when they deserve it, but they do it with blacks.)
    Is this pattern of discrimination morally objectionable, and is it in particular a reason to abolish the death penalty?
    You can’t say it is if you believe only in non-comparative desert. Then abolition would only make the situation worse — instead of there being just some people who are getting less punishment than they deserve (I’m assuming for the sake of argument that some crimes deserve the death penalty), there would be more. And that was actually used by Ernest van den Haag as a response to the argument from discrimination to abolition; he said abolition on this ground would be a case of “two wrongs make a right,” i.e. unjustified.
    But if you believe in comparative desert you can say there’s something bad in itself in the fact that people who are equally deserving are not receiving equal punishments. And if the inequality can’t be removed by ensuring that the whites do get the death penalty (biased juries just won’t do that), that can be an argument for abolishing the death penalty.
    And it precisely was part of the argument when the US Supreme Court temporarily declared the death penalty unconstitutional in the 1970s, on the ground of its discriminatory application. One of the the justices said that even if the discriminatory pattern meant only that whites who deserved the death penalty were not getting it, the inequality in the application of the punishment was unjust and had to be removed, in particular by (at least temporary) abolition. That has to be a comparative and not non-comparative claim.
    The relevant quote from the Court decision is in an article of mine in the Olsaretti volume on Desert and Justice. That article also contains a more sophisticated account of comparative desert than Shelly considers, one involving not just the positive idea of proportionality (the best division of goods according to comparative desert) but also the negative idea of contraproportionality (the worst division, e.g. where the twice as virtuous person suffers twice as much pain). Adding contraproportionality handles a lot of Shelly’s counterexamples, e.g. the ones about how much more virtuous A should suffer if less virtuous B is suffering. But Shelly doesn’t discuss it in his book — I’m not sure why.
    And I think the two scales in the account — for what’s deserved and for its desert-basis — have to have negative values, below non-arbitrary zeroes. Pleasure and pain are surely relevant to well-being, and pain is the contrary of pleasure, with a non-arbitrary zero between them. Likewise vice is the contrary of virtue, again with a non-arbitrary zero between.
    Some years ago I discussed Shelly’s counterexamples involving ratios with zero in the denominator with the mathematician who gave me the idea of contraproportionality and showed me how to display it in a graph. He said mathematicians don’t worry about cases with zero in the denominator — they crop up all the time and require a special clause but are otherwise no big problem. At least that’s what I think he said — it was a while ago!
    But everyone should read Shelly’s book. It’s so much not the same old, same old.

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