William M. Briggs

Statistician to the Stars!

Equality Is Impossible: Part I

There is a certain way that philosophers talk that make them sound, to outsiders, like they’re spouting nonsense. Take David Miller, for example. He writes on the subject of equality in Philosophy and Politics:

Complex equality…recognizes a number of relevant dimensions along which individuals may be scored, but it does not insist that scores be equalized along any dimension in particular. Instead it claims that overall equality can be achieved by counterbalancing among the different dimensions. If the dimensions are independent, in the sense that there is no connections between how a person performs on one and how he performs on others, then relative gains in one direction can be set against relative losses in another.

A professional philosopher will know that Miller is merely summarizing the learned literature on “equality theory.” But a lay or uninformed reader will presuppose that the man has lost his mind. Do philosophers really say that equality—the sublimest of all goals—can be had if only we could look into each heart and weigh or score each dimension of desire, awarding to each what he wants in proportion to how these rewards fit in with what each other persons’ desires?

They do say so, but you must understand that in philosophy we often discuss situations that might happen, that are theoretically possible, no matter how unlikely they might be. For example, we can imagine a Star Trek-like transporter device, and then ask questions about what happens if such a machine existed, all the while acknowledging that building such a device is next to impossible. So Miller might be talking theoretically and therefore might not be as nuts as he sounds.

Could we then imagine a device—never mind if we could actually build the thing—that at each and every moment, looks into each person’s heart, weighs all his desires and fears, and then looks into the world to see what resources are available, computes the means of manipulating those resources to turn them into “products”, and then, for each person and across all people simultaneously, metes out both the work required to manipulate those resources and to then to deliver the “products” before, of course, each person’s fears and desires changed?

Don’t get caught up in the improbability of the thing—it is clearly only a fantasy. But fantasies drive actions, so it’s important to understand it for at least that reason. It’s also necessary to ask whether such a thing could be done “in theory”, because if it can, then we can figure how close to the ideal we can get.

So is Miller’s equality of fulfillment possible? I think the answer is no, it is not. And the reasons are simple.

Suppose everybody got it into their head that they wanted to live in a certain spot and that living in that spot would fulfill their deepest desire. It doesn’t matter whether this situation is probable either, but clearly it is possible. Thus, by a kind of people-Pauli exclusion principle, equality is impossible because not all people could live in one spot, even if the “spot” is generously defined as a rather large plot of land.

Now, this spot could be on the surface of the sun (we can imagine building a shelter to weather the heat) or it could be on a beach in Hawaii. But no matter where it is, everybody can’t fit there.

Suppose next that my soul’s desire is to have X, where X can be an object like a certain baseball card, say, or X could be a state of affairs such as my enemy put six feet under, or, human nature being what it is, X could be a certain amorous relationship. Although somewhat loosely defined, X is unique. That is, there are some Xs which no two people can possess simultaneously. Somebody is going to go wanting.

These are two of the theoretical reasons why equality of fulfillment is impossible. Not just unlikely, but impossible. Of course, there are a host of reasons why it is impractical: no man can fully articulate his desires nor anticipate perfectly his needs, there would never be universal agreement on the desire-duty weighting algorithm, resources could never be manipulated into products and delivered quickly enough to satisfy that algorithm, and on and on. Even stronger, any scheme of equality always fails at least on age and sex: that is, everybody isn’t the same age and sex, and nothing can be done about that.

Equality of fulfillment isn’t the only definition of “equality”, but we will find (as we examine this subject over a series of articles) that of all the common definitions, none are possible, even in theory.

20 Comments

  1. Not only impossible, but also a complete straw man.

    As a sometimes-extremely-leftist person, I do not see the goal of politics to build a society were “equality” is a goal. I do see extreme inequality as a symptom of something rotten in economics – a derivation that few right wingers admit , but that’s completely different.

    No, for me, a good politic goal for the 21st century is to abolish famine in the world. Now this is very specific and too little “abstract” for the post in question, but I think that we should pose these issues concretely, so that we know what we are talking about. I don’t mind living in a society where rich people exist and buy islands, etc. But I do mind living in a diminishing world where returns for the middle and poor classes are lessening and lessening, where the corporate world has abolished pretty much any employee’s weapon of fighting back, where the new generations have to work pretty hard just to survive under precarious wages and conditions, and of course, where there is just so much famine and poverty around the world.

    These are real problems, and to state that to solve them is “impossible” is completely ridiculous. Fortunately, you haven’t done so, and I do hope that you didn’t imply it, not even subliminally…

  2. “…none [of the definitions] are possible..”

    . Hmmm. Looking forward to reading more. Have always enjoyed some of Eric Hoffer’s intuitive thinking, ie.

    “We can be absolutely certain only about things we do not understand”.

    , which I interpret as tending to confirm your premise.

  3. There is, of course, a variant of the prior two reasons why equality is impossible based on uniqueness or shortage of supply: my preference is to be unequal to you. Normally this means “better than” but I suppose in some circles of misery, “worse than” may be preferred. My guess is that Arrow’s theorem also excludes the possiblilty of equality if one of the preferences is not to be dictated to by any other.

  4. Well, we could all have our DNA changed… towards a single solution. We would be a lot more equal then. Of course, we would still have our different memories and environmental differences…

  5. Luis:
    Wouldn’t procreation be a bit of a problem if we all had the same DNA?

  6. Consider that the “grass is always greener”. For instance, suppose Briggs and I are the exact same, with just a couple of differences. I am much more attractive, while he has a blog that a couple people read every day. These things might balance each other out, but instead I am distraught over my pitiful writing talent, while Briggs is content with his mediocre appearance. So are we equal? Or is Briggs better off? Obviously, since Briggs is content, he should pay me money to even things out. I will not rest until he is just as upset as me. Then we will be equal.

  7. Can we really imagine a human, much less a group of humans, in which the individual or individiuals maintain constant heartfelt values about a variety of things, including the relative value/desirability/etc. between & among the factors being measured?

    …didn’t think so….

    Which illustrates that while the thought exercise may be valid for the parameters [& admittedly unlikely groundrules] presented one also needs to keep in mind that the animal upon which it is focused, an animal displaying a consistent & stable set of values/outlooks/etc. doesn’t exist.

    That aside:

    “Equality of Fulfillment” as presented in this blog assumes that this means the same for everybody — and reality is quite different. The Declaration of Independence addresses equality in terms of basic interests–life, liberty, and the pursuit of happiness. But at no point does it or any other governent document define what end-state “happiness” is achieved at. And for good reason — its different for everybody.

    Thus, a debate in which a particular end-state being defined as the same for everybody, or considered as possibly being the same for everybody (e.g. Mao’s ubiquitous & thus trendy & fashionable grey pajamas) carries the implicit presumption that many if not most people don’t know what will make them happy & need to be told; absent that they take cues from those around them. Adolescents manifest this “independence” from authority by behaving as predictable pack animals (fashion, music, accoutrements, etc. all pretty much the same)…and eventually many outgrow it. Those that don’t become Democrats and look for some idol to tell’m what they like/want/and “should” have & value.

    See: www. libertymind.com

  8. Bernie, we would all be females and our children would be clones of us inseminated.

    Alas, to the future :D

  9. Luis:
    Where is the fun in that. I could make a comment about it being a typical killjoy leftie solution, but you are too nice a guy and too self-reflective for me to make such a comment. ;)

  10. I applaud Adam H’s insightful analysis. Isn’t the role of government to distribute misery evenly, therefore achieving the social goal of level outcomes?

    “..building such a device is next to impossible.”

    What is next to impossible? Totally improbable?
    .

  11. I think the whole question is not well posed – as is usually the case with philosophy. My desires are to a large but indeterminate extent a product of my history and my environment, not a property of me as an individual. With a different history or within a different environment, my desires would be different.

    So the search for equality, while somewhat admirable, does nudge us towards a state of affairs where we have roughly the same history and live in roughly the same environment. I don’t think this is what we desire.

  12. Is this really what Miller means by complex equality? Reading the blurb, it sounds like he is saying that there exists a metric by which 2 different distributions could be declared equal.

    And I thought that complex equality meant that e^πi = -1

  13. Tufty:
    The question may not be well posed, but I am not sure you need to introduce from whence our preferences come even though it helps you make a point with which I viscerallly agree. As others habve pointed out, many show a preference for being different.

  14. relative gains in one direction can be set against relative losses in another.

    This assumes, of course, that the quantity of gains along different axes are commensurable. But as Doug M hints at above, for something as straightforward and well understood as the complex plane there is no amount of imaginary that equals any amount of real; the complex numbers do not possess a partial ordering. Translating this into the domain of human qualities: how much red hair is a misshapen toe equal to or how much aquiline nose can you balance off against one black eye?

    That leaves us with the task of defining some sort of functional that maps the quantity of gains along different directions to another set which does possess a partial ordering, like, for example, the magnitude of a complex number which maps the complex number to a real number (in fact it maps many complex numbers to the same real number). At that point the simplistic notion of “complex equality” falls apart and we’re back to square one.

    My philosophical education began and ended many years ago with a couple of courses from Paul and Pat Churchland and I don’t believe that they would have made a bone-headed mistake like this. Is the current crop of philosophers particularly dull or merely innumerate?

  15. This assumes, of course, that the quantity of gains along different axes are commensurable.
    .
    I would also go along this comment and the complex plane analogy is not bad .
    Actually I would prefer a Hilbert place countably infinitedimensional .
    In this case the perfect equality is a sphere in the Hilbert space and the measure of inequality is given by the measure of the difference between the volume of your personnal spheroid and the perfect , absolute , quasi divine equality sphere .
    The difficulty being , of course , that as mentionned by The Man , the equality space of the philosophers and politicians is not a Hilbert space because it contains vectors that are NOT measurable .
    .
    This is the main reason why all the fighters-for-happiness-and-equality finish by being Marxists if they take it seriously .
    Indeed the only coordinate that is not only measurable but ordered is the economical coordinate . Earnings , property , taxes – all that can be measured and ordered .
    The equality here makes mathematical and therefore logical sense .
    I am absolutely certain that , like the AdS/CFT duality , a theorem can be proven that ANY socio-economical theory aiming at economical equality which can be rigorously and mathematically defined is isomorphe/reduces to Marxism .
    .
    And Marxism has been falsified by empirical evidence .
    Hence I submit the conjecture that demonstrates William’s statement reduced to economy : “As every economical equality theory is isomorphe to Marxism , economical equality doesn’t exist .” ;)

  16. I did some reseach on “equality theory” and it seems to come down to the idea that “rewards” should be perportional to “contributions.” But should contributions be measured only by effort. Or should contributions be Effort * Skill?

    These equality theorists don’t like luck. But as long as output is dependant on the weather, then we can never escape uncertanty. Add in war, technology, and fashion — Risk and rewards for risk cannot be ignored.

    It seems to me that many naturally occuring phenominon exhibit an exponential distribution. Money is one of them.

  17. If any one man and one system can be said to have defeated famine, it would be Norman Borlaug and the “rightwing” USA. Compare and contrast Borlaug’s and America’s achievements vis feeding the world to those of his contemporary, Trofim Lysenko, poster child of the Extreme Left.

    It is FACTS like those that tend to discredit Marxists and other collectivist Utopians. Farming is a business, a capitalist business, and those who would kill capitalism end up killing their own countrymen, by the tens of millions.

    Not that the intentions of Marxists are necessarily evil incarnate. Just their outcomes. But they do achieve equality — the legions of murder victims are almost indistinguishable from each other.

  18. Mike’s caricature is funny… until someone takes it seriously of course. To say that Lysenkoism is a “poster child” of the Left is just as ridiculous as stating that Hitlerism is the poster child of the Right Wing. But that’s what happens when you make extreme statements like that: you open yourself to the ridiculous.

  19. I think it was Hayek who stated that it was for the better that “Luck” existed. For the thought of living in a perfect “meritocracy” where everybody believed that if I owned a Ferrari, then that would be because I “deserved” it, would be unbearable and inhuman. I agree with him. Chance makes life bearable.

  20. Luis describes himself as “a sometimes-extremely-leftist person” who’s goal is to “abolish famine in the world.”

    But the extreme leftists in history (Stalin, Mao, Pol Pot etc.) have inflicted famine on their own enslaved populations, starving tens of millions of people to death.

    So excuse me if I get CDD (cognitive dissonance disorder) from Communists who claim to be anti-famine, when induced famine has been their modus operandi for 100 years and their famine victims number in the tens of millions.

    I don’t find Luis to be ridiculous; I find him to be murderous, along with his Communist brethern. Communists do not feed the world, they starve the world. American capitalist farmers fed Russians when the Commies managed to cripple their internal capacity to feed their own people.

    But let’s just forget about all that, and accept the Commie lie that they want to “end famine”. Forget about the mass graves. Forget about the millions of dead babies. Forget about the insanity that is Communism. Modern Commies are different — NOT!

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