As regular readers will know, CT blogger Ingrid 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.
{ 24 comments }
GG 07.29.23 at 6:24 am
JQ –
It looks to me like the math above works at any point on the income distribution. You can always increase aggregate utility by decreasing income for the top earner and increasing income for some number of other earners. But that, in turn, leads straight to Parfit’s Repugnant Conclusion. Am I wrong?
John Q 07.29.23 at 6:56 am
Parfit’s repugnant conclusion is logically separate, since it involves adding people to the population, unlike the examples here, which are only repugnant from the POV of billionaires.
Parfit’s argument is also wrong, for reasons similar to the wrongness of Nozick on the utility monster. I’ve started a separate post on this, in the context of McAskill and longtermism. I’ll try to get it done soon.
Greg Ball 07.29.23 at 6:58 am
As a lapsed physicist I got a thrill from reading this!
GG 07.29.23 at 7:25 am
JQ@2 –
Looking forward to reading that forthcoming post.
Regardless of whether Parfit’s argument is directly on point, there’s not anything particularly special about using a billionaire in the example above. The same result obtains if you start with a person of modest means, and redistribute half of their income to the immiserated in Darfur. The math works out the way it does based on relative inequality wealth; I don’t think it says anything about limitariansim per set.
John Q 07.29.23 at 9:30 am
GG, you’re right that the argument is general. Limitarianism is a special case.
As I said, the shorter version is that utilitarianism implies limitarianism. More precisely, you need utilitarianism + net negative externalities from the very rich’
Ingrid Robeyns 07.29.23 at 10:09 am
Thanks for this John. Isn’t it the case that classical utilitarianism implies equality of outcome? (that is, if the only thing that were to count is the average or the total of people’s ‘utility’, and in a static world). Limitarianism is weaker than equality of outcome (it allows for some inequalities) so for me this isn’t a surprising result (but perhaps I’m overlooking something).
Many of the people I meet who argue against limitarianism assume that the world is better-off with with the billionaires – hence they assume that the processes that their wealth above the limit generated has, on balance, beneficial effects for others. But there are so many reasons to think of why this isn’t true (they fill several of the chatpers in the book I wrote – done and dusted but unfortunately not in the bookshops before Feb 1st). Looking forward reading the next post you want to write on this, John!
(PS: I’m travelling to various places over the next 2 weeks so am not sure I will be able to further engage here, but am very much looking forward reading your further thoughts on this).
oldster 07.29.23 at 10:40 am
“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.”
Ah, Bentham, right. The one who said,
“The question is not, Can they reason?, nor, Can they talk? but, Are they strong and capable? Why should the law refuse its protection to any being with sufficiently similar strengths and capabilities?”
Pittsburgh Mike 07.29.23 at 11:07 am
I think the problem with this note is visible from the first sentence: a limit on what one person “can own or consume.” There’s a big difference between own and consume. Bezos owns 10% of Amazon worth about $135B, but that’s not something he’s consuming in any sense.
Taking Bezos’s share of Amazon and giving it to the 99% would be just as inflationary as simply issuing $135B in treasuries, depositing it with the Fed and giving that money to the 99%. Bezos, because he can’t/won’t spend that money himself, has taken his wealth outside of the money supply. The USG, if it wants, can make up for it by effectively printing money and giving it away itself.
Of course Bezos has some control over Amazon from his ownership, but he’s going to do what anyone else owning it (at least anyone not named ‘Musk’) would: try to make it as successful as possible.
So, if there’s really something better to do with Bezos’s wealth, the USG can just do it, since Jeff has kindly locked his money up in a box.
BenK 07.29.23 at 11:39 am
Assumptions that need to be unpacked especially include the link between $$ as wealth or income and resources. As anyone knows who has bought a pair of shoes, say, the link between cost at time of purchase, price when sold used, and utility, is not at all linear. You can spend ~$5 for a used pair of shoes, $5,000 for a new pair of shoes, and all the range in between. However, only the very rich see any impact to utility from buying a pair of shoes that is more than $500, and even for them, it may not close to a 10x increase. It certainly didn’t take 10x resources on margin to create those shoes, though it may be effectively impossible to reproduce the brand and heritage and all those things that mark them with class signifiers at even 1000x resource investment over the short term.
The same goes for all sorts of goods and services.
John Q 07.29.23 at 11:47 am
Pittsburgh Mike: I think you are conflating two issues. First, there’s the distinction between wealth (a stock) and income (a flow). For the economy as a whole, and for most non-poor people, wealth >> income. But you can make the argument either way.
The other is the idea rich people don’t consume much of any additional income. That’s true in the short run. But in the long run, people at all income levels consume most of their income . This was a big issue in C2o debates over the consumption function.
Ingrid, thanks for kind comments. For a given aggregate income, equal distribution maximizes utility. But in a market economy, there’s a limit to how much redistribution you can do without reducing total income. So, you need to think about predistribution as well.
Pittsburgh Mike 07.29.23 at 12:57 pm
Do rich people really consume most of their income? That I think is the key question, and one that I don’t really know the answer to.
It’s hard for me to say, since I doubt my wife and I are typical: I’ve added to my savings even when I was a poor-ish grad student in 1978 living on a tax free $350/month ($1563/month today). My wife and I have always saved a significant chunk of our income, and over the last 5 years I’m sure we’ve saved way more than half of our after tax income. And probably half of our expenses were paying list price for our two kids’ college and grad school tuitions, which I view as a charitable contribution to those schools :-)
Certainly someone with Bezos’s wealth should be able to extract 5% of their wealth each year, which for him would be $6B/year. I’m not sure it’s physically possible for him to spend that much money on personal consumption for him and his family.
So, I think that some of the wealth owned by the top 0.1% is effectively locked up enough that national governments can just spend it without risking inflation.
MisterMr 07.29.23 at 1:19 pm
It seems to me that utilitarianism does indeed imply equality of outcomes, but only as much as the process that causes the equality of outcome causes disutility in itself: e.g. if Hardworking Bob gets exactly the same money than Lazy Sam, then there is no reason to be harworking, everyone becomes lazy, and everyone loses (this is probably the same pont that JQ is making in 9).
I mostly agree with this argument, however I think that “utilitarianism” is more an abstract philosophy that tries to give a definition of what is “good”, rather than a specific political philosophy, because when you put it in pratice it is so difficult to give a definite calculation of utility that one can justify both soviet-style communism and free market fundamentalism (because utilitarianism also is consequentialist, so if free market fundamentalism causes much higer income for everyone it still works for utilitarianism).
“the assumption that people are sufficiently similar in capability and strength that they must all be taken into account equally”
This is actually all you need to get utilitarianism IMHO. In fact, it would be enough to say “we should weight all people’s interests and satisfaction equally, and use this as the misure of good” and this would already entail utilitarianism (which under common assumption would still entail limitarianism if applied to the economics, but this would be a different use).
Tim Sommers 07.29.23 at 6:21 pm
Utility is not not about “compar[ing] different allocations of resources.” Saying it’s about the effect of various allocations of resources is closer. One thing is for sure, it can’t be that there’s no such thing as utility – else what are we talking about? It could be an aggregate or only approximate, but it can’t be nothing or just anything. As I am sure you know, the most common views of utility are as happiness, preferences, or an objective list theory (your resource view being one of them).
More importantly, the declining marginal utility of resources gets you close to limitarianism all on its own, if you start as a utilitarian. But nothing takes you all the way. It’s always possible that there are cases, however improbable, where it makes sense for the utilitarian to ignore limitarianism. For example, suppose due to “the overview effect” getting yourself launched into orbit hugely increases your utility. Now suppose we live in a society where everyone is very well-off. You might not have anything to do with some excess cash that would not meaningfully increase your utility and I might be just a little short on launching my rocket, so that if you gave me that money I’d be better off without making you worse off while exceeding the upper limit.
Who cares about such stylized and ridiculous counter-examples (see utility monster, too)? Philosophers do because they allow you to distinguish various views. Look, most positions people take on distributive justice have similar outcomes over most “normal” cases. Despite the brouhaha over Rawls difference principle it only rarely gives a different outcome than utilitarianism. And economists and political scientist don’t urgently need philosophers because its pretty clear, for example, that justice urgently demands a less unequal distribution of wealth. The details can wait. Basically, strict equality, sufficientarianism, prioritarianism, and limitarianism give similar answers over most realistic cases. I always try to emphasize this to my students and hope they take it to heart. Then I go back to teaching philosophy and explain that utilitarianism is very different from limitarianism, even though they overlap in their judgements about many cases.
John Q 07.29.23 at 7:44 pm
“strict equality, sufficientarianism, prioritarianism, and limitarianism give similar answers over most realistic cases.”
This is pretty much true except for sufficientarianism, which implies a lot more tolerance of inequality (depending on how you define “sufficient”). But it seems to me that a lot of people attracted to prioritarianism and limitarianism are hostile to utilitarianism in part because they don’t understand its implications.
But this list scarcely exhausts the range of widely held views. Natural rights theories, classical liberalism, virtue ethics, and most forms of conservatism give support to inequalities of various kinds.
Graydon 07.30.23 at 12:29 am
One does also need to consider that there comes a point with great wealth where it can completely ignore feedback, and so the general economic utility of the great wealth becomes negative.
There are obvious examples in fossil carbon extraction and policies of starving out strikes. The objective is (at best) one of control, and at worst one of creating notional profit by the involuntary transfer of actual costs to other parties.
LFC 07.30.23 at 4:30 am
Most of the math I might have learned I’ve forgotten, but I don’t find this post to be crystal clear. At one point JQ says that an extra dollar is worth more to a poor person than a rich one. Then in the next paragraph he says that a given increase or reduction in income has the same value whoever receives it. These two statements seem to contradict each other.
Were Bentham, Mill or other utilitarians particularly concerned about economic inequality? If the basic utilitarian principle is to maximize the sum total of happiness, pleasure, or the satisfaction of rational desire, that might or might not have egalitarian implications depending on how the “utility” to be maximized is defined, and whether certain satisfactions are weighted more than others (cf Mill on higher and lower pleasures). The fact that you can reduce and redistribute Musk’s wealth/income with no reduction in total utility doesn’t, istm, prove anything. What you have to show is that redistributing Musk’s wealth would increase total utility. Maybe the OP does show that, but if so I didn’t find it esp clear.
John Q 07.30.23 at 4:46 am
LFC. “Then in the next paragraph he says that a given increase or reduction in income has the same value whoever receives it”
The crucial missing word is “proportional”. An increase of a dollar on an income of $100 a week is 1 per cent. To get the same proportional increase at $1000 a week you need $10. And so on.
Reread with that in mind, and see if the post makes more sense to you. If not, I’ll try to clarify
Tim Sommers 07.30.23 at 10:17 pm
Thanks for responding. Always enjoy your posts. You’re not wrong, but…
I am not sure prioritarians are all that hostile to utilitarianism. Rawls treats it as the view to beat, but is constantly flattering it. Parfit who named and defends prioritarianism is also a utilitarian (though I admit I don’t know how that is supposed to work).
I should have said “distributive” theories, I guess. Once you think the distribution of wealth matters, there’s a convergence (I would argue). As far as the other views you mention…
Plausible virtue theories (Nussbaum and Sen) put limits on allowable inequality.
As for conservatism, to the extent that is a coherent, cohesive theory of justice it is natural rights or classical liberalism. Further, the difference between natural rights and classical liberal/libertarian views ain’t much either. There’s basically distributive views and entitlement views. Again, if you think that there is an answer to the question what the distribution of wealth and income (and some other currencies) should be, answers cluster and give similar advice on most normal cases.
John Q 07.31.23 at 6:29 am
Thanks for these useful comments, Tim.
I wanted to come back one more time on extreme examples like the utility monster, which I never find convincing.
In Ingrid’s discussion of limitarianism she says (can’t locate the quote now) that it is a rule intended for the world we live in, and worlds like it. In a world without scarcity, we wouldn’t need to impose limits (though we might advise moderation). But that’s not our world.
I think of utilitarianism the same way. In a world with utility monsters, most non-monsters would probably reject utilitarianism. But that’s a scope limitation, not an argument against utilitarianism in our world, or worlds like it.
Paul Segal 07.31.23 at 9:56 am
Tony Atkinson famously developed this idea with his inequality index, which has a parameter that allows you to decide how inequality-averse you are. With that parameter equal to 1 you get the logarithmic utility you use here. Then the higher the parameter, the more inequality-averse you are, meaning you place still less value on the marginal dollar going to the rich compared to the poor.
The neat thing is that you can determine your own favoured Atkinson parameter using the “leaky bucket” thought experiment. You ask: how much income would I be willing to lose (e.g. through deadweight loss of taxation) in order to transfer income from someone with $1000 to someone with $100. If you are indifferent between taking 10 from the first in order to give 1 to the second, it means you don’t mind losing 9 in deadweight loss, and you are in Bernoulli’s log case with an Atkinson parameter of 1. If you are more egalitarian and would be willing to lose 9.9, meaning you would take 10 from the rich to give just 0.1 to the poor, your parameter is 2; if on the other hand you are less egalitarian and would only take 10 from the rich if you can give 5 to the poor then your parameter is 0.3.
Some key open questions: this is entirely based on relative incomes, and we might think the absolute level matters too – e.g. if the poverty line is $150 we might choose differently in the above experiment than if the poverty line is $500.
Also, for me the main battleground would be whether we think there is such deadweight loss anyway: there are strong reasons to think redistribution does not, overall, cause significant deadweight loss – e.g. if reduced work incentives for the rich are outweighed by increased work capacity for the poor.
Tim Sommers 07.31.23 at 4:13 pm
I agree with you.
I wanted to mention one last thing that seems relevant. Forgive me for expressing it poorly. Maybe, these are just intuitions that I picked because of the way things are now, but it seems to me that utilitarianism is ethics for institutions whereas Kant et al are the ethics of individual behavior. For one thing, you just don’t have access to the kind of information you would need to be a real act utilitarian daily. And, on the other hand, at the extremes the hell with an absolute prohibition on anything. (One problem, ofc, is that people are always claiming whatever happening is an emergency situation.) I think I am sort of agreeing with your original post by saying that utilitarianism almost always gives approximately the right answer. To put it rigorously. LOL
John Q 07.31.23 at 7:29 pm
Tim 221 “ethics for institutions” is exactly what I was trying to get at when I said utilitarianism is a political philosophy.
Paul, this is useful. And an important implication for the post is that, even with an Atkinson index well below 1, the main point remains valid. I’ll try to do some maths on this.
engels 08.10.23 at 11:29 am
Shocked to see the Utility Monster getting the trolley treatment… If you don’t like the Utility Monster how about the Pooular Person? He (or she) has lot of friends/fans when s/he smiles we all smile with him/her. Does this mandate a super-sized consumption basket? Not an academic question perhaps in the age of the influencer…
engels 08.11.23 at 12:30 pm
if Hardworking Bob gets exactly the same money than Lazy Sam, then there is no reason to be harworking, everyone becomes lazy
An alternative scenario is where Starvin’ Marvin gets less money and can’t afford the education/medicine/urban housing he needs to be productive so his job is done by Mediocre Marmaduke, who just happened to be better off initially and to live in London.
Comments on this entry are closed.