Rawlsekianism Reloaded Part IIa: The argument for Maximin (or Leximin)

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  1. Avatar Mike Schilling says:

    Unfortunately, part 2 started to take up lots of space and had to be split up. Part 2a […]

    You are George RR Martin and I claim my 10 pounds.Report

  2. Avatar Jason Kuznicki says:

    I have great difficulty with the idea that the way to go about formulating a theory of justice is to start with distributions we might like to see, regardless of the personal qualities of the individuals receiving them. Few things are less fair than lotteries, and the only thing that makes them tolerable at all is that the participants are willing — a condition that wouldn’t apply to a world run on Rawlsean principles.

    Consider that some folks surely deserve to be in prison. But if I adopt a maximin strategy, am I not required to abolish even the institution of the prison, for fear I might end up in it?Report

    • Avatar Murali in reply to Jason Kuznicki says:

      Consider that some folks surely deserve to be in prison.

      Surely I do. And as Chris says below, there are good ways to justify brisons without appealing to desert. But here, I’ll give you 3 good reasons why we shouldnt appeal to desert from the very outset.

      1. Desert (if not justified in various careful contexts or justified pragmatically) comes with a lot of metaphysical baggage. This is metaphysical baggage which we cannot, as of yet (if ever), incorporate into the theory (or any theory of justice which could hope to serve as a point of agreement whatever people’s metaphysical claims could be).

      2. You don’t want to be trying to justify market institutions with respect to desert because you are going to run into trouble with gift giving and inheritances (at the very least)

      3. There is a place for desert, but it is in the 4th judicial stage (the first is the original position, the second and third are the constitutional and legislative stages respectively. The veil of ignorance is slowly pared away as we progress through the stages with more and more specific information about the social conditions being revealed.Report

    • Avatar Murali in reply to Jason Kuznicki says:

      Also one thing to note is that when trying to find out what the moral principles are, it begs the question to assume some moralised notion like desert. And the principles of jsutice, at the end are moral principles.Report

  3. It seems to me that people go behind a veil of ignorance on a regular basis and do not in fact choose a maximin ordering.

    For example, I have plans tonight to make a 25-mile round trip solely for the purpose of engaging in a recreational activity. There is a very small but nonzero chance that I will be severely injured, and perhaps even killed, in an automobile accident en route.

    Alternatively, I could stay home. I will probably not have as much fun, and I certainly won’t meet any pretty girls, but I’ll almost certainly be safer. The odds of my being killed or severely injured will be much, much lower.

    When deciding whether to make this trip, I find myself behind a veil of ignorance. I don’t know which position I will occupy in the set of all possible outcomes.

    The maximin principle would suggest that I should stay home. Actually, with a probability-agnostic veil of ignorance, the maximin principle has nothing to say about this scenario at all, because in either case the worst-case outcome is death. Which is part of the reason why a probability-agnostic veil of ignorance is problematic.

    Let’s suppose for the sake of argument that the probability of death if I stay home falls to zero, so that there is some maximin-based distinction between the two scenarios. The maximin principle suggests that I should stay home. The worst-case scenario if I stay home is that I don’t have much fun, which is very strongly preferable to dying in an automobile accident.

    But I’ve chosen to go out, and in doing so accept a very small risk of a very low payoff (injury or death) in exchange for a higher average payoff (fun!) and a small chance of a very high payoff (meet future wife). And people do this all the time.

    That Rawls’ principles do not accurately model people’s revealed preferences is highly problematic. And I think that the two primary reasons they fail to do so is that they don’t account for probability and that they give lexicographical superiority to improving the worst-case outcome. There’s a margin at which any reasonable person is willing to accept a worse worst-case outcome in exchange for improving other possible outcomes, but where that margin is depends on the probability distribution.Report

    • Avatar Murali in reply to Brandon Berg says:

      but where that margin is depends on the probability distribution.

      Brandon. In the previous post we discussed this. There is a reason why we obscure the probabilities in the veil of ignorance. This is because a choice to for example optimise the position of the better off at the expense of the worst off just because we happen to calculate that the probability of ending up in the worst off category is very low fails to justify that such is appropriate as a principle of justice. If I know who I’m going to turn out to be, or have some reasonable probability estimates, then of course I will pick out a principle that is biased in my favour. (given the assumption that I am self interested only) One of the major reasons of the veil of ignorance was to prevent the parties from employing self serving bias.

      That Rawls’ principles do not accurately model people’s revealed preferences is highly problematic.

      Look, maximin is certainly not the optimal strategy in cases involving knightian risk (where the probabilities are known). Maximin only becomes rational when all the probabilities are completely unkown. i.e. at the limit of complete knightian uncertainty. Of course, at intermediate levels of risk and uncertainty, some mixed strategy is likely to be better.

      Moreover the question is not whether maximin models what we tend to do in situations of uncertainty, the question is whether its optimal. (i.e. the is-ought distinction)Report

      • Avatar Brandon Berg in reply to Murali says:

        If I know who I’m going to turn out to be, or have some reasonable probability estimates, then of course I will pick out a principle that is biased in my favour.

        But it’s not biased in your favor, specifically, since you have the same payoff distribution as everyone else. The reason you choose it isn’t that it gives you some special advantage—it’s that overall it’s a preferable distribution, despite the fact that its minimum payoff is worse than some other lower-variance distribution.

        If everyone is willing to make that trade-off ex ante, then isn’t it kind of crazy to say that the principles of justice require us all to pick a distribution that nobody really wants while behind the veil?

        For it to be biased in your favor, you’d have to be assured of a high relative position in the distribution (e.g., at the 90th percentile). The point of the veil of ignorance is (or should be, anyway) to force people to consider the possibility that they might occupy a low relative position in the distribution, not to obscure important information about what the payoff distribution looks like.

        Maximin only becomes rational when all the probabilities are completely unkown.

        I’m not sure I’d even go so far as to say that. When probabilities are unknown, there’s no basis for rational choice. So maximin isn’t even rational then.

        Moreover the question is not whether maximin models what we tend to do in situations of uncertainty, the question is whether its optimal. (i.e. the is-ought distinction)

        My point is that it is optimal. People don’t violate the probability-agnostic leximin decision process irrationally; they do it because the probability-agnostic leximin decision process is flawed.

        This is obvious if you push it to extremes. Consider two distributions:

        A: 99.9999% chance of payoff of 10, 0.0001% chance of payoff of 0.
        B: 100% chance of payoff of 1.

        Assuming that 1 is a terrible payoff only slightly better than 0, any reasonable person would choose distribution A. A society with distribution A is clearly a better society to live in than society B.

        Or consider:

        C: 99.9999% chance of 10, 0.00001% chance of 1.
        D: 0.0001% chance of 10, 99.9999% chance of 1.

        C is unambiguously preferable to D, but a probability-agnostic veil of ignorance obscures any distinction between the two.Report

        • Avatar Murali in reply to Brandon Berg says:

          When probabilities are unknown, there’s no basis for rational choice.

          Not according to the literature.

          http://www.kangsungan.pe.kr/upfiles/dissert/a08_14.pdf

          despite the fact that its minimum payoff is worse than some other lower-variance distribution.

          The key thing to note that it is not necessarily the case that leximin will result in a lower variance distribution. Leximin can countenance massive inequalities as long as it improves the position of the worst off.

          My point is that it is optimal. People don’t violate the probability-agnostic leximin decision process irrationally; they do it because the probability-agnostic leximin decision process is flawed.

          This is obvious if you push it to extremes. Consider two distributions

          I dont see the point of pointing out that what is the optimal strategy when probabilities are known differs from the optimal strategy when probabilities are unknown.

          I think you’re missing the point here. Probabilities are obscured in order to model certain (very general) moral constraints into the original position.

          The issue is not that the parties are agnostic about probabilities, but that they not only don’t know the probabilities, but cannot know the probabilities. Now, unless you define rationality so narrowly as to work only within the confines of precisely known probabilities, then clearly, some strategies for working under varying degrees of uncertainty are more optimal than others. Merely showing that our strategies under uncertainty are going to be different from those under risk does not show anything.

          Saying ex-post when the veil of ignorance is lifted that the parties would have chosen otherwise if they had known more about the actual conditions in society fails, therefore, to appreciate the moral argument just made against utilitarianism.

          Finally, in the OP, we are not choosing what type of society we would be living in, rather we are choosing the principles of justice.

          C: 99.9999% chance of 10, 0.00001% chance of 1.
          D: 0.0001% chance of 10, 99.9999% chance of 1.

          The point where we choose what society we want to live in is in the second stage (the constitutional stage) in which more specific information about the society is available. Of course in the 2nd stage, we can note that there are more better off in C than in D, fewer who are worse off in C and no concommitant decrease in welfare of the worst off. Sensitive to this context, of course the difference principle would encourage choosing C over D.

          The distinction drawn here between the first and subsequent stages has to do with the fact that at their base, moral principles are universals, even though they apply in a context sensitive manner.Report

          • Avatar Brandon Berg in reply to Murali says:

            The point where we choose what society we want to live in is in the second stage (the constitutional stage) in which more specific information about the society is available.

            But knowing that the leximin has the potential to lead us horribly astray in the second stage, why would we agree to it in the first?

            Sensitive to this context, of course the difference principle would encourage choosing C over D.

            But it would still require us to choose B over A, wouldn’t it?

            I dont see the point of pointing out that what is the optimal strategy when probabilities are known differs from the optimal strategy when probabilities are unknown.

            The point is that leximin encourages us to choose a society in which all are wretched (B) over a society in which one is wretched (A). Knowing this, it is clear that leximin is not, in fact, the decision process that rational people would agree to behind the veil of ignorance.Report

            • Avatar Murali in reply to Brandon Berg says:

              But it would still require us to choose B over A, wouldn’t it?

              Maybe, maybe not. More needs to be said about what 0,1 and 10 are. If 0 is slavery and 1 is abject poverty…

              The point is that leximin encourages us to choose a society in which all are wretched (B) over a society in which one is wretched (A).

              Omelas! Enough said.Report

  4. Avatar stillwater says:

    Excellent! Bringing Rawls to the masses!

    Seriously, tho, Tim K’s posts on what constitutes liberalism and conservatism, and of course the general disarray of libertarians in accepting any principles and sticking to them made me wonder what I think is a reasonable and defensible take on liberalism. And of course, I thought of Rawls. His writing is something I both accept and feel comfortable defending and am quite happy to refer folks to as expressing liberal principles and thought.

    (I’ll prolly have substantive comments to make after going over it more carefully.)Report

  5. Avatar Chris says:

    Few things are less fair than lotteries

    I don’t have much desire to defend Rawls, because I’m not a Rawlsian, but I will note that yes, this is precisely Rawls’ point (ToJ has a long discussion about the lottery of birth).

    Consider that some folks surely deserve to be in prison. But if I adopt a maximin strategy, am I not required to abolish even the institution of the prison, for fear I might end up in it?

    No, this takes a simplistic view of the leximin reasoning going on behind the veil. Rawls goes into punishment in ToJ, though I cant lay out his reasoning well from memory (I tried for a few minutes): suffice it to say that one of the assumptions will be the need for at least a minimum level of protection from violators, so prisons do become necessary, even from a maximin perspective.Report

  6. Avatar BlaiseP says:

    Without going too far into the math (mostly because I’m not sure how much math HTML this site supports), there are some big problems with the payoff schemes, especially in the probabilities. Nonetheless, this is a good piece and well-considered.

    I’d like to put forward what I call the Seurat Solution. Seurat was a pointillist painter, applying dots of pure color to large canvases: the images he produced are best seen from a considerable distance. Seurat was a scientific man, acquainted with the work of Chevreul. Forgive the blockquote from Wiki, it really does make a difference here.

    Chevreul was a French chemist who restored old tapestries. During his restorations of tapestries he noticed that the only way to restore a section properly was to take into account the influence of the colors around the missing wool; he could not produce the right hue unless he recognized the surrounding dyes. Chevreul discovered that two colors juxtaposed, slightly overlapping or very close together, would have the effect of another color when seen from a distance. The discovery of this phenomenon became the basis for the Pointillist technique of the Neoimpressionist painters.

    Chevreul also realized that the ‘halo’ that one sees after looking at a color is actually the opposing, or complementary, color. For example: After looking at a red object, one may see a cyan echo/halo of the original object. This complementary color (as an example, cyan for red) is due to retinal persistence. Neoimpressionist painters interested in the interplay of colors made extensive use of complementary colors in their paintings. In his works Chevreul advised artists that they should not just paint the color of the object being depicted, but rather they should add colors and make appropriate adjustments to achieve a harmony. It seems that the harmony Chevreul wrote about is what Seurat came to call ’emotion’.

    Rawls and his Veil of Ignorance are fairly easy to subsume into this metaphor: each dot is one tiny and self-interested peek through the Veil and doesn’t tell you much. But each peek is important, since we cannot fully understand what any one person finds important in life, what the optimal payout might be for them, personally.

    In the real world, beyond what you or I or anyone else might consider fair and just, the Law accretes Precedent unto itself, often breaking off large chunks of what was previously settled law, growing new branches to adapt to new problems. Here, the Seurat Peek gives some insight: as each case before the courts is settled, based on precedent, judges (especially in non-adversarial systems such as France where the judge is essentially the prosecution) still have enormous discretion, applying their own reasoning abilities to derive justice for each case, the totality of the law notwithstanding. The judge does not say “Oh well, I have found four defendants guilty this week, I suppose I ought to find the next defendant innocent to provide some semblance of fairness, lest I get a reputation as a hanging judge”, though he very well might grow increasingly vexed by the draconian verdicts he renders by dint of the laws which state he must obey some Three Strikes law or the like.

    The reason Rawls’ Veil works so well is because we can all place ourselves in the dock with the defendant and demand due process and the right to face our accusers and present exculpatory evidence, to defend our own good names and property from slanderers and squatters. We would like to say the justice done in our name must reflect facts, not mere speculation. But there will never be truly disinterested parties to any such case: we are all biased in favor of our own preferred outcomes. Utilitarian philosophy always founders on the reefs of justification: each decision requires some axiom of fact which must be justified by other such facts in an infinite regression and as the old lady said to Bertrand Russell about cosmology, “it’s turtles all the way down”.

    Religion has always known possessions were a problem. What is truly ours? The more we have, the more we must defend from others. Possessing becomes a full time job: it becomes a justification for all sorts of selfish behaviors. Now I am no Buddhist, declaring the lust for money and possessions a sickness, though I do believe that lust corrupts people’s souls. If some have plenty and others have nothing, something is more intrinsically wrong with that society than mere redistribution will correct.

    Operating within the realm of the possible, I observe for the worst-off to improve in the slightest, the most well off must profit immensely and I have no problem with that. Capitalism is not a zero sum proposition. There is simply no excuse for starvation and abject poverty anywhere in the world. Show me famine and poverty and I will show you a fucked up government ruled by incompetent despots. Granted, you may not see many rich people, but as economies variously flourish and wither, the entire population slides up and down the yardstick of wealth. Class warfare is ignorant troublemaking in the main, but there are societies which try to preserve their aristocracy through the systematic denial of education to the poor. It never really works, though. Ultimately such aristocracies decay and are replaced, for such aristocracies don’t educate their own progeny and they become effete.

    For at the terminus of great wealth, once all the hedonistic pleasures of life have been enjoyed and found wanting, is the greatest pleasure, philanthropy, and it seems to be a constant in human history. Bill Gates, while he ruled the Microsoft Empire was a ruthless man who inflicted great harm on the world at large with his brain-dead and insecure operating system, stifling his competitors and belittling his employees. Yet his great wealth (and that of Buffett) now goes (among many other good works) to find a cure for malaria: who would have thought it? The Gilded Age featured many such monsters, Gould, Fisk, Rockefeller: look where their money went.

    The lottery is an insufficient metaphor. Justice and fairness are not lotteries, they are dynamical systems: the rain falls on the just and the unjust. Rawls’ critique of utilitarian philosophy supposed each person’s gauge of personal happiness was different. My personal happiness would be for someone to endow me to work on the manuscripts of Monte Cassino: give me a little apartment in Rome and a pass to the Vatican Library and I should be content. That’s my little Seurat Peek. Everyone gets annoyed with me for injecting personal anecdote into the discussion hereabouts, but I am grimly amused by this phenomenon. What do these pedants want? For me to reduce my argument to some algebraic argument when life is mostly the black box of calculus? Reality is individually perceived and each Seurat Dot is part of an indivisible whole, each jagged shard of the hologram containing the whole. There is no Veil. We will only arrive at justice when we perceive ourselves in others, obeying the Platinum Rule, treating people not as we want to be treated, but as they want to be treated. Rawls’ Veil is actually a vast canvas, hiding nothing, containing multitudes, in which each of us must play our own distinct part, obeying the principles of mercy, not justice. Justice is easy: we switch sides. Mercy is hard: you’re thirsty, have a drink from my canteen.Report

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