The limitarian implications of utilitarianism

A bit wonkish, but important

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 follows

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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.