My fellow Crooked Timber blogger Ingrid Robeyns has long been making the case for limitarianism, that is, the idea that there should be an upper limit on the amount any one person can own or consume. As Ingrid has observed, limitarianism is a constraint, rather than a complete ethical principle, so it’s important to consider how it interacts with other principles. In the case of utilitarianism, the answer is surprisingly well, at least in (using Ingrid’s terminology) this and nearby worlds. But understanding this requires a little bit of background and some arithmetic.
Shorter JQ: utilitarianism implies limitarianism. The full argument is over the field (no tricks this time, I promise).
First, utilitarianism is a political philosophy, dealing with the question of how the resources in a community should be distributed. And it starts, as in Bentham, from the assumption that people are sufficiently similar in capability and strength that they must all be taken into account equally. This does not, in itself, imply equality of outcomes or even opportunity, but it rules out notions that some group is inherently deserving of better treatment than others.
Second, (this shouldn’t be necessary to state, but it is), there is no such thing as utility. It’s a theoretical construct which can be used to compare different allocations of resources, not a number in people’s heads that can be measured and added up. Nonsense about “utility monsters” and similar is just that.
The practical implication of this is that we need a measure which answers the question: how does the benefit of giving an additional unit of resources to one person compare to the benefit of giving those resources to another. A utility function is a way of answering that question.
There is an ethical judgement here which can be addressed in various ways. We can take a Rawls/Harsanyi original position, rely on introspection or look at people’s choices over time and under uncertainty. None of these are perfect, but most yield one clear conclusion: marginal utility declines with income or, more simply, an extra dollar is worth more to a poor person than to a rich one. But how much more?
The classic answer to this question, going back to Daniel Bernoulli, is that we can think of utility as a logarithmic function of income (or wealth). What that means is that a given proportional increase (or reduction) in income has the same value whoever receives it. Most recent estimates are similar. So, utilitarianism suggests converting everyone’s income to its logarithm and adding them all up. This may sound mechanical but the implications are striking.
What does this mean for limitarianism? If we take a centibillionaire such as Elon Musk, his wealth is of the order of 10^11. Using base-10 log (it doesn’t change anything if you use another base such as the natural log), and and assume that their wealth neither benefits nor harms anyone else [more on this], we get a contribution of 11 to aggregate utility. If his wealth were reduce to say, $1 million, utility would drop to 6.
Now suppose we take five people, chosen anywhere in the income distribution, and increase their wealth by a factor of 10. This would exactly offset Musk’s loss of utility.
To take a less artificial example, consider the 5000 workers Musk sacked from Twitter when he took it over. An increase of .001 in utility for each of them, which would require an income increase if 10^.001 = 0.2 per cent, would offset Musk’s loss.
So, classical utilitarianism gets us to the point where we should place (effectively) zero value on additional income accruing to the very rich. To get to limitarianism, we only require that the extra wealth of the rich is, on balance, undesirable for the rest of us.
The converse is the “trickle down” model that we will all be better off if we allow the rich to get rich. As I argued in Zombie Economics, the evidence of the last 40-50 years doesn’t support this view.
John Quiggin 
I assume the upshot of this is an argument for greater equality by prohibitively taxing the very rich and redistributing to the poor. The story ignores production and the welfare impacts of the implied redistributions to make your arguments work. .
First off you should be writing about consumption not wealth or income. Elon Musk’s wealth is irrelevant from a welfare viewpoint if it is mainly invested in firms that provide good incomes for workers and which, on the basis of his ideas and imagination as well as his capital, produce goods (such as electric vehicles) that reduce the effects of climate change. I pick an environmental good but it wouldn’t change the argument if Musk produced a popular brand of salted peanuts. What matters is the consumption of the wealthy not their wealth (or indeed their income if that income is mainly saved and productively reinvested).
Of course too, with confiscatory taxes beyond a certain level of wealth or income there may not only be less savings by the wealthy and hence lower wages on the weak assumption that capital and labour are complements. There may also be reduced incentives to make effort that seeks to increase wealth or income among the wealthy. In so far as these reduced incentives reflect socially-worthwhile productive activities society loses. There are aso effects on the incentives to work and save for those on lower incomes who work less because they receive redistributions from the wealthy.
It is difficult to envisage situations where extra income or wealth among the very rich disadvantage the rest of the community. If they save most of the wealth they earn then that increases wages and benefits those on wages. Even if they spend it on goods these are produced elsewhere in the economy augmenting the demand for labour. There is seldom, or probably never, a pure loss when the wealthy get more.
The argument you propose is for a pure exchange economy without production where incentives to work are irrelevant. It is totally a priori – an abstract model of the type you like to try to finesse that doesn’t get welfare analysis anywhere.
Admitting production there are no strong value-free egalitarian principles. Probably the strongest argument for taxes is that, if we seek to fund a given level of public spending, we should ignore wealth and concentrate on consumption. Then consumption taxes are better at addressing a bad economic situation than taxes on wealth. Penny-pinching rich people generate lots of social advantage. The costs of being wealthy arise only if they spend too much.
I’ve been arguing for wealth limits for many years. I predicted we would fail to stop climate change under unfettered capitalism and its dangerous concentrations of wealth. Wealth isn’t just wealth. It is power. A major use, perhaps *the* major use of great wealth is for power. The concern with Rupert Murdoch or Elon Musk (for examples) is not how many dinners they will eat. The concern is how their decisions (to push fake news and toxic views on msm and social media for examples) affect billions of people and ultimately the global environment very negatively. This influence is so baleful that humanity is about to destroy itself at the behest of billionaires, all the while worshiping them and idolizing excess wealth for its own sake.
We have seen the effects of Musk’s wealth power re Twitter. He can buy and break something because he can. Twitter had positives and negatives. It even had a sort of commons aspect. Too bad. Musk smashed it because he had the capital power to do so. If it wasn’t intentional then it was inept, on a grand scale, revealing perfectly why so much capital power, including money from private investors, should not be in the hands of one man.
On the issue of Australian housing, as another example, why should some people own ten houses (picking a number) while ten people own no houses, solely or jointly? Many of the people who can’t buy houses are hard working young couples, both in good employment, living sensibly and saving hard. “Only feckless fools are poor” is a self-serving myth of the rich: rich by inheritance, luck, lobbying or swindling, as often as not. The current economic policies, like negative gearing, which massively favor capitalists over workers, are now ensuring that the relatively few get to own the houses while the many save indefinitely, chase rising deposit requirements and likely will never own a house, at least until their baby boomer parents die.
“It is difficult to envisage situations where extra income or wealth among the very rich disadvantage the rest of the community.” Wrong. One doesn’t need to imagine examples. There are plenty of real examples in the really existing economy as per the housing example. “Very rich” is a relative term. If you own two houses then you are very rich compared to those who own no houses. If you own one house then you are very rich compared to those who sleep under a bridge.
HC said: “It is difficult to envisage situations where extra income or wealth among the very rich disadvantage the rest of the community.”
Difficult to envision for some Harry, not difficult for Ikon I believe, nor I.
Or others for example.
^2. JQ: “the accumulation of massive fortunes, particularly in the finance sector, have become a drag on economic growth.”
^1. Nicholas Birdsong: “Societies with pronounced economic inequality suffer from lower long-term GDP growth rates, higher crime rates, poorer public health, increased political inequality, and lower average education levels”.
*
^1.
“The Consequences of Economic Inequality”
2015
…
“In unequal societies, government support tends to decline for public education programs. As the rich become increasingly wealthy, public policies become increasingly favorable to the policy goals of the economic elites.[65] Public education programs tend to be unpopular with the wealthy because they involve taking public funds, which often primarily consist of taxes imposed on the rich, and redistributing those resources to the poor.[66]
“The beneficial effect of increased GDP growth correlates with higher rates of inequality. From the perspective of the wealthy or liberal economic theorists, fairness is maximized in economically stratified societies that avoid redistributive policies. However, the disadvantages of economic inequality are more numerous and arguably more significant than the benefits. Societies with pronounced economic inequality suffer from lower long-term GDP growth rates, higher crime rates, poorer public health, increased political inequality, and lower average education levels.
https://sevenpillarsinstitute.org/consequences-economic-inequality/
^2.
“The coming boom in inherited wealth”
“Are we creating a society Jane Austen might recognise?
JOHN QUIGGIN
…
“One particularly striking piece of evidence, drawn from a study by economists Richard Reeves and Isabel Sawhill, is that rich kids who make bad choices do pretty much as well as poor kids who do everything right.
“Indeed, we have probably already passed the point where the growth of inequality and the accumulation of massive fortunes, particularly in the finance sector, have become a drag on economic growth.
…
“Whether we like it or not, the patrimonial society seems to be on its way.”
https://insidestory.org.au/the-coming-boom-in-inherited-wealth/
To get a proper handle in this I’d have to read 5+ books and twenty articles. Yet like not knowing what porn looks like, I know it when I see it. In my opinion.
JQ: “To get to limitarianism, we only require that the extra wealth of the rich is, on balance, undesirable for the rest of us.”.
If I could make extra wealth “undesirable for the rest of us”, I’d have just solved for humanity.
Which to me invokes acceptance by both the majority and minority of The Greatest Happiness Principal “”The less the numerical difference between the minority and majority, the more obvious the deficiency in aggregate happiness will be (1983a, 309)”.
Happy to be corrected.
*
From:
“Jeremy Bentham
…
“Greatest Happiness Principle
…
[Betham:] “Be the community in question what it may”, … “divide it into two unequal parts, call one of them the majority, the other the minority, lay out of the account the feelings of the minority, include in the account no feelings but those of the majority, the result you will find is that to the aggregate stock of the happiness of the community, loss, not profit, is the result of the operation”.
“The less the numerical difference between the minority and majority, the more obvious the deficiency in aggregate happiness will be (1983a, 309). Logically, then, the closer we approximate the happiness of all the members of the community, the greater the aggregate of happiness.”
…
https://plato.stanford.edu/entries/bentham/#GreHapPri
KT2, What I said was that the wealthy getting wealthier did not disadvantage those less wealthy if the wealthy invest in capital assets which strengthen the wages of those less wealthy. You need to think about that claim and drop your foolish disgust at my rejection of conventional woke ideas. I stick with my claim.
KT2, What I said was that the wealthy getting wealthier did not disadvantage those less wealthy if the wealthy invest in capital assets which strengthen the wages of those less wealthy. You need to think about that claim and drop your foolish disgust at my rejection of conventional woke ideas. I stick with my claim.
If the wealthy get wealthier but don’t invest in capital assets, does that disadvantage those less wealthy? If the wealthy get wealthier and do invest in capital assets but those capital assets doen’t strengthen the wages of those less wealthy, does that disadvantage those less wealthy?
If capital and labour are substitutes – e,.g. the case of robotics – then my claims don’t hold up. Maybe small positive effects on wages in the sector producing robots.
Is the wealth of wealthy people mainly invested in firms that provide good incomes for workers?
How many firms do provide good incomes for workers? What is a good income, anyway?
What, then, is the consumption of the wealthy?
To what extent is it the case that efforts to increase wealth or income among the wealthy take the form of socially worthwhile productive activities? How would it be possible to tell?
Perhaps it’s difficult for you to envisage, but I’m fairly sure that some people have found it much easier to envisage.
It’s intriguing when somebody (in this case Harry Clarke) makes an argument which is totally a priori, without any presentation of empirical evidence whatever, and then complains about other people doing that.
In this I read the small in number upper middle class taking aim at the yet smaller in number rich. It’s a blinkered view held widely by the privileged top 20 percent or so that in their apprehended shared adversity they too are part of the 99 percent missing out and being left way behind by the 1 percent. Musk gets a mention, of course, but university professors, for example, do not. The top 20 percent have a proclivity to lump themselves with the bottom 80 per cent as being similarly left behind by the one percent. They are keenly observant of the widening wealth gap between them and the 1 percent, and with gaze fixed there are indifferent to the widening gap opening below between them and the lower 80 percent, and the societal damage arising.
“So, classical utilitarianism gets us to the point where we should place (effectively) zero value on additional income accruing to the very rich. To get to limitarianism, we only require that the extra wealth of the rich is, on balance, undesirable for the rest of us.”
No, in fact the extra wealth of the top 20 percent (at least) is undesirable for the rest of us. It is about there from where any limiting ought begin.
Richard Reeves has it that:
“Focusing on the top 1 percent is a mistake. The real class divide is between the upper middle class—the top 20 percent—and the rest of America.
…In fact, it is the Americans in the top fifth of the income distribution—broadly, households with incomes above the $112,000 mark—that are separating from the rest. This separation is economic, visible in bank balances and salaries. But it can also be seen in education, family structure, health and longevity, even in civic and community life.” – Richard V. Reeves, May 30, 2017, The Dream Hoarders, in Boston Review https://www.bostonreview.net/articles/the-dream-hoarders-how-americas-top-20-percent-perpetuates-inequality/
The OP and Reeves’ focus on persons and the situation in the US, yet it is just as applicable to Australia and other developed, supposedly affluent countries. Housing affordability and precarity, food, health, education and taxation are a few of the obvious areas where the top 20 percent are a distinct privileged class who may gripe about the increasing wealth gap between themselves and the 1 percent, but who as a class are increasingly separated from and work against the bottom 80 percent and with likely greater societal detrimental effect than the 1 percent.
Without limits to inequality being applied soon for the greater good and societal order, and with numerous tripping factors such as climate and food shortages looming all around, we are closing in fast on Peter Turchin’s mathematical projections of our civilisational end times.
https://aeon.co/essays/history-tells-us-where-the-wealth-gap-leads
https://www.penguin.com.au/books/end-times-9780241637791 (the preface and most of Part 1 on preview at the amazon link)
https://peterturchin.com/twenty-years-of-cliodynamics/
Svante,
The upper middle class in Australia are, in the main, operating as you say. Though I do think most people who blog here and who may be UMC probably vote and/or act directly in attempts to help the lower 80% and especially the lower 20%. Overall, a large section of the upper 19% plus all the upper 1% are the problem. Agreed.
Just happened to have seen this article this morning re another topic. Seemed relevant.
“The coming boom in inherited wealth
“Are we creating a society Jane Austen might recognise?
JOHN QUIGGIN
21 SEPTEMBER 2021
…
“One particularly striking piece of evidence, drawn from a study by economists Richard Reeves and Isabel Sawhill, is that rich kids who make bad choices do pretty much as well as poor kids who do everything right. Poor university graduates have only a 20 per cent chance of ending up in the top 10 per cent of earners, marginally greater than the chance of rich high school dropouts ending up there.
“The combination of these various findings yielded the new and much gloomier picture of inequality presented most clearly in Thomas Piketty’s Capital in the Twenty-First Century,…
…
“Australia typically follows the United States, with a lag. Between 2003 and 2017, the most commonly used measure of wealth inequality, the Gini coefficient, rose from 0.57 to 0.62 (the higher the number, the more unequal the wealth). By 2017, the top 20 per cent of households held 63 per cent of all wealth. Ownership of shares and other financial assets is particularly concentrated; with asset values increasing faster than wages, this implies an increase in the importance of inheritance.
….
https://insidestory.org.au/the-coming-boom-in-inherited-wealth/
Svante, utilitarianism also justifies redistribution from the top 20 per cent, as you can easily see if you can work with logarithms. The point of this post was to show that it implies limitarianism for the same reason.
With respect John , utilitarianism does not imply redistribution from the top 20% at all if you engage in economics and allow for production and for the disincentive effects of the redistributions both for welfare recipients and for their providers with or without log-linear SWFs. And these are the issues economics has somewhat inconclusively pondered for decades. In the past you have objected to the use of lump-sum redistribution assumptions in welfare economics. One can say you are restricting your attention to pure exchange economies where lump-sum non-distortionary transfers can be made and this might be an academic exercise but it has no policy implications. You need to get back to the core economics of incentives/disincentives and the impact of changed savings by the wealthy on the incomes of those less wealthy via effects on capital stocks that change labor’s productivity. .
I think there is nobody thinking seriously about these issues who advocates “going after” the 1% only.
IIRC Robeyns found that there is (more or less) consensus that a family fortune of 1-2 million euros is “enough”, so we could use that as a starting point.
Some non-utilitarian arguments for a more equal income/wealth distributions:
– getting rich is mostly luck (Sandel), so wealth is undeserved
– rich people got rich using the infrastructure paid for by all of us (Obama: “You did not build that road”)
– money = power which corrodes democracy (as mentioned above)
It is worth mentioning the Lauderdale Paradox in this context. I highlight this concept periodically. It really is the key to understanding the shell game swindle that is capitalism.
“James Maitland. 8th Earl of Lauderdale, wrote an “Inquiry into the Nature and Origin of Public Wealth (1804 and 1819)”, in which he introduced the concept that has come to be known as the “Lauderdale Paradox”: there is an inverse correlation between public wealth and private wealth; an increase in the one can only come at the cost of a decrease in the other.” – Wikipedia.
And now for a long quote showing basically how enclosure of the commons and other stratagems create the artificial scarcity which generates private wealth and public poverty.
“In the paradox with which his name came to be associated, Lauderdale argued that there was an inverse correlation between public wealth and private riches such that an increase in the latter often served to diminish the former. “Public wealth,” he wrote, “may be accurately defined, — to consist of all that man desires, as useful or delightful to him.” Such goods have use value and thus constitute wealth. But private riches, as opposed to wealth, required something additional (i.e., had an added limitation), consisting “of all that man desires as useful or delightful to him; which exists in a degree of scarcity.”
Scarcity, in other words, is a necessary requirement for something to have value in exchange, and to augment private riches. But this is not the case for public wealth, which encompasses all value in use, and thus includes not only what is scarce but also what is abundant. This paradox led Lauderdale to argue that increases in scarcity in such formerly abundant but necessary elements of life as air, water, and food would, if exchange values were then attached to them, enhance individual private riches, and indeed the riches of the country — conceived of as “the sum-totalof individual riches” — but only at the expense of the common wealth. For example, if one could monopolize water that had previously been freely available by placing a fee on wells, the measured riches of the nation would be increased at the expense of the growing thirst of the population.
“The common sense of mankind,” Lauderdale contended, “would revolt” at any proposal to augment private riches “by creating a scarcity of any commodity generally useful and necessary to man.” Nevertheless, he was aware that the bourgeois society in which he lived was already, in many ways, doing something of the very sort. He explained that, in particularly fertile periods, Dutch colonialists burned “spiceries” or paid natives to “collect the young blossoms or green leaves of the nutmeg trees” to kill them off; and that in plentiful years “the tobacco-planters in Virginia,” by legal enactment, burned “a certain proportion of tobacco” for every slave working their fields. Such practices were designed to increase scarcity, augmenting private riches (and the wealth of a few) by destroying what constituted public wealth — in this case, the produce of the earth. “So truly is this principle understood by those whose interest leads them to take advantage of it,” Lauderdale wrote, “that nothing but the impossibility of general combination protects the public wealth against the rapacity of private avarice.”” – John Bellamy Foster and Brett Clark.
https://monthlyreview.org/2009/11/01/the-paradox-of-wealth-capitalism-and-ecological-destruction/
If the existence of effects has been conclusively established (whether that’s by economists or by anybody else), then it could be a problem for an analysis if it neglects the impact of those effects where they are relevant. But if all that’s happened is that the possible existence of some such effects has been inconclusively pondered (whether that’s by economists or by anybody else), then the case is different.
For example, if we can be absolutely sure that there are positive consequences for the poor when the rich get richer, then that could be a good reason to hesitate about trying to stop the rich from getting richer. However, if all that’s happened is that some people have speculated about the possible existence of mechanisms which could result in positive consequences for the poor when the rich get richer, that’s no reason for the rest of us to pay deference to their speculations.
KT2 (JULY 31, 2023 AT 3:38 PM), thanks for that linked article. I had read it, and appreciate the refresher. I must say it is not surprising that Prof JQ was across Reeve’s work before my recent exposure arising from Reeve’s “Dream Hoarders” being mentioned in one of the growing number of reviews (Guardian, I think) of Peter Turchin’s recent “End Times: Elites, Counter-Elites and the Path of Political Disintegration”. In the “Inside Story” article immediately following mention of Reeve’s and Sawhill’s findings JQ mentions Thomas Piketty’s “Capital in the Twenty-First Century” and the findings and dismal prognosis for the future of society and mass of humanity. Picketty’s empirically based work is also a small part of a much wider range of empirical historical data from numerous disciplines drawn on by Turchin. Most reviews and my own limited sampling agree that ”End Times” is rather well written for its target fairly innumerate audience. It seems it will present the findings, conclusions, and projections of a highly complex technical study in an approachable style. It will be a good read, probably a best seller. My city library has two copies on order and though I thought I got in pretty quick at 32 in the que on hold clearly I was not quick enough! Might have to buy this one – the hypothesis, analysis, and projections are fascinating. A good society desirous of continuing should certainly be mindful.
JQ, you may have to write a book, or get an addendum to “chapter 1 of Bayesian Data Analysis”
http://www.stat.columbia.edu/~gelman/book/
Bekiw from “Fully Bayesian computing: Don’t collapse the wavefunction until it’s absolutely necessary.” at Andrew Gelman’s blog, statmodeling.
It seems to me from article, marketers are using Utility as a number in people’s heads that can be measured and added up.
Andrew Gelman said “This all seems very standard to me and is implied by basic simulation summaries, as described for example in chapter 1 of Bayesian Data Analysis. Regarding people’s concerns: yeah, you shouldn’t first summarize simulations over people and then compare people. What you should do is compute any quantity of interest—for example, a comparison of groups of people—separately for each simulation draw, and then only at the end should you average over the simulations.
“Sometimes we say: Don’t prematurely collapse the wave function.”
Kevin Gray, who prompted the post writes;
“This is highly relevant because since the late 90s it has been common practice in marketing research to use these individual-level “utilities” to compare preferences (i.e., relative importance of attributes) of pre-defined groups or to cluster on the utilities with K-means (for example).
From “Fully Bayesian computing: Don’t collapse the wavefunction until it’s absolutely necessary.”
Posted on August 4, 2023 9:01 AM by Andrew
“Kevin Gray writes:
“In marketing research, it’s common practice to use averages of MCMC draws [^fn1] in Bayesian hierarchical models as estimates of individual consumer preferences.
https://statmodeling.stat.columbia.edu/2023/08/04/fully-bayesian-computing-dont-collapse-the-wavefunction-until-you-have-to/
^fn1 – MCMC
https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo