Future Wealth Inequity

My last two posts described inequality in firm and city sizes, and in individual wealth. Today, firms and cities are quite unequal, following a Zipf distribution, with a tail power near one (giving a very thick tail.) Individual wealth is a bit more equal, with a bigger power of ~1.4 (and hence a thinner tail).

This distribution of firms and cities seems to result from their being tolerably effective across a wide range of sizes, having long unequal lifetimes, having little net local growth, and holding a roughly fixed total number of people. In contrast, individuals have more equal lifespans, are psychologically inclined to spend more as they get richer, and have spending habits that correlate only weakly across generations. (“Rags to rags in three generations.”)

How might these change in the future? In the em era, I expect firm distributions to stay similar, but expect city and individual wealth distributions to change. I’ve talked before about how I suspect strong gains to em concentration, as they suffer less from travel congestion, leading perhaps to most being in a few dense cities. In this post, let me talk about em wealth.

Since em lifespans should be limited mainly by em wealth, em lifetimes can vary a lot more than human lifetimes, and ems can have more long-term spending consistency. While some ems will spend their wealth on more copies, others will hoard their wealth. Some may even manage to consistently reinvest most of their wealth via something like a Kelly criteria. This seems likely to make future em wealth evolution more akin to today’s firm and city evolution. I thus expect a near Zipf distribution for the high tail of em wealth.

This change in tail power should make em wealth distributions more unequal. Under a tail power of ~1.4, today’s richest person has about $75B, which is about 0.04% of the world’s $200T wealth. Under a power of ~1, the richest person might be about a hundred times richer, holding ~4% of the world’s wealth, or $7.5T.

Since a Zipf distribution has an unbounded expected value, its inequality also depends on the total population size (which follows it). The following table shows this dependence:

The “% of Richest” column says what fraction of the total wealth is held by the one richest person. The “MidW %” column shows the (smallest) fraction of the population that holds half of the total wealth. And the “MidW/ave” column shows how much richer is the mid-wealth person (for whom half of all wealth is held by richer folks) than the average person.

For a Zipf wealth distribution, as the population gets larger wealth gets more concentrated. Even so, the very richest person holds a smaller fraction of the total wealth. The same should apply to firms and cities if they retain a Zipf distribution — the firm and cities that hold most people will get larger, even though the largest firm or city would be a smaller fraction of the total.

In sum, as the population gets larger, I expect firms and cities to get larger.  And for “immortal” ems, I also expect a more unequal distribution of wealth. Even so, as population increases the very largest firms, cities, and rich folks should hold smaller fractions of their respective totals.

Added 11p 14Jan: This post has now been up for a whole day, with zero comments and one vote. Which has to be some sort of record for reader disinterest. This is especially noteworthy, given that I’m especially proud of this post, culminating several days work trying to understand something important about the future. Alas that I  sometimes bore readers, but I’m writing this blog mainly for me, so I’ll continue to write about what most interests me, even if past responses suggest readers won’t be as interested.

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  • Earlier you’ve said humans shouldn’t worry about ems because we’ll survive off our accumulated wealth a la retirement. But over time won’t ems come to control nearly all the wealth? And since ems are so fast, “over time” might not be long. Individuals can live off their accumulated retirement funds for a limited period of time, it’s questionable whether that could indefinitely sustain biological humanity.

    • As the economy grows, the human faction of wealth could become small, even as its amount stays constant or grows. Imagine if we still had ten million original immortal foragers around today – they wouldn’t need to own much to have a comfortable retirement.

      • This is true, assuming their currency wasn’t limited in value by inflation, or depleted by parasitic legalized “raids” or “seizures.”

  • richard silliker

    I find some of your comments to be very HiO, abstractions of abstractions.

    Perhaps a simpler secular language would help in building the bridges necessary. This may engage others to respond.

    And you could continue to post.

  • richard silliker

    Zipf distribution

    After a Goggle of Zipf distribution my feeling is that statistics should be a controlled substance.

    Use the “force” Robin.

  • Jayson Virissimo

    Sometimes we don’t comment because we don’t have anything interesting and true to add, not because the post isn’t interesting itself.

  • This post has now been up for a whole day, with zero comments and one vote. ….

    Well, 90% of the post is describing the Zipf distribution, which isn’t controversial; it’s just a math object. I’m not sure what people could add. I’m sure if you spent more time on the speculative part—that em wealth will have a zipf power roughly like that of firms rather than humans—there would be more to talk about. Better yet, make some normative claims and we’ll really get people fired up.

  • Jason

    A question: your definition of inequality differs from the continuous case of Pareto distributions; inequality is measured by the Gini coefficient which is directly related to the exponent. Given a particular exponent for the distribution, inequality (as measured by social scientists) should be constant.

    Second: http://arxiv.org/abs/cond-mat/0002374

    In this paper, inequality (Pareto exponent/Gini coefficient) is directly related to the volatility of markets (and exchange), and not population:

    exponent = 1 + exchange/market volatility

    Where exchange = fraction of wealth exchanged per transaction
    and market volatility = variance of Gaussian distribution of returns

    Of course, this is a specific model. However, it does give a mechanism for producing a Pareto distribution of wealth.

    • The paper you link explicitly shows that inequality is a constant as population varies only for a power greater than one.

      • Jason

        That is true, but aren’t we in a mu > 1 situation? I believe the models in the paper, both the simple and “more realistic”, have mu > 1 in the mean field. There is a wealth condensation phase transition for mu infinity, but I don’t know if that is a realistic scenario (although I guess in the case of quadrillions on ems we might reach that scenario).

        ps I also just noticed you linked to this paper in your previous post so you were already aware of it — I am just back from a trip, and going through my RSS feed in reverse chronological order. Sorry for jumping in without being up to date.

      • Jason

        There is a typo, “mu infinity” should be “mu < 1". (Pretty far off!)

  • Steve

    I read most of what you write, vote occasionally and rarely comment. I find your blog to be the most radical and thought provoking of those I read, I hope you continue to write about that which you find most interesting.

    • Explodicle

      Same here. FASCINATING, groundbreaking work. I just get to it days later when the discussion has gone cold. I particularly enjoy your post-em projections.

  • Michael Wengler

    I may not have commented but I opened some links and read about zipf and city population distributions and so on. The post on wealth where you connect the distributino to a model of wealth increasing and decreasing… I had no idea whether the connection of the distribution to the dynamics was a necessary one, and indeed it seemed it was not. But I wasn’t going to understand it until i spent some time beating the math to death, and my interest in this topic didn’t extend to that kind of time commitment. (I have a day job beating other math to death as an engineer).

    Then THIS post, using Zipf dynamics I don’t grok or believe to talk about a theoretical world with quadrillions of ems in which I don’t really believe either, what would I say? I read the post, looked for stuff I could care about or think was close enough to reality to provide useful insights, and moved on.

    I can also tell you I have rarely noticed the recommendation button, probably NEVER used it, and often read your posts a few days after they are posted, this post i have not read until now.

  • Question 1

    Leiji Matsumoto was on to something.

    • Question 1

      Arg, looks like the video was taken down. This is the official site but you have to manually jump to 2:00 in the video.

  • What a great analysis of what was part of concern #3 in our list here: http://www.33rdsquare.com/2012/01/top-five-singularity-concerns.html

    “Would the “99%” enjoy their servitude while only the elites become post-human? “

  • ChrisA

    Robin – you are never boring, but you can be a bit intimidating at times. Maybe that’s why you only got a few responses.

    I continue to argue that in an AI world, the ability of AI’s to modify their own software, including their moral program, rapid evolution and an arms race will quickly end up with one person destroying all others, so the world will be very unequal with that one person holding all wealth. Any AI that didn’t take the approach of becoming a superparanoid power grabber, will be quickly eliminated. This explains the doomsday paradox pretty well.

    With the additional premise (a pretty strong one I submit) that any intelligent race will achieve AI before interstellar travel, thus solving the Fermi paradox as well.

  • Mr. Econotarian

    Future income inequality is likely to rise (c.p.) because of rising global wealth. Those who are best able to create and sell innovation will have a larger market to sell in to and will generate more income.

    Those who do not create and sell innovation due to lack of motivation, intelligence, or government regulation will have their own limited skills cannibalized by growing technological innovation.

  • CliffR

    What other areas besides size/wealth do you think this might extend to, even if they can’t be explicitly modeled? Knowledge comes to mind, both at the top end and expansion of “intellectual laypersons,” and maybe some form of social capital…?

    Otherwise, to clarify the “disinterest:” You crossed multiple fields of academics to tackle an ambiguous question prompted by exactly no one, framed your findings relevant to major issues, such as 21st century population dynamics and wealth distribution, and although all this required some serious effort and candle power, shared the most significant takeaways as concise, intriguing insights of personal interest when nearly all others in academia seem to only concerned with getting their work published.

    Nobody else drops Big Knowledge like that. So please excuse the delay in processing these posts, but often my thoughts are left too incomplete at first to even “Like” them in good conscience. Unless, of course, I’d be giving a thumbs-up for Intellectual Balls, but that’s why I come to this blog in the first place.

  • majus

    I have a question, kind of from left field. I just read Robert Reich’s “Aftershock”, from which I personally took away the concept that the trend towards increasing concentration of wealth is at the root of unpleasant trends in our society and economy. He finishes the book with a workmanlike plan to reverse the trend.

    I frankly haven’t studied statistics or economics deeply, so pardon the naivity of this question: is there an underlying law or set of conditions that would make Robert’s goal unfeasible?

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