"Each Counts for One"

Why aggregation is ethically fundamental

Last year, I published a paper in Philosophical Studies called “Each Counts for One.” Marcus Arvan kindly invited me to write a blog version of it for New Work in Philosophy, his terrific Substack. Equally kindly, he gave me permission to cross-post on BIG iff TRUE.

---

With housing costs rising worldwide, some loyal readers of this newsletter may have resorted to living under a rent-controlled rock. Even so, I bet you’ve heard of the Trolley Problem.

Here’s the classic Bystander at the Switch, meant to illustrate that killing one to save five isn’t always wrong.

Thomson (1985)

Or perhaps you prefer the legendary Footbridge, which illustrates the wrongness of physically putting people in harm’s way.¹

“The single most famous and well-worn case from all of twentieth-century normative ethics,” per Caspar Hare (see Thomson 1976, 1985)

You may also have stumbled on noncanonical “Trolley Problems,” as in:

One moral of all this Trolleyology is that people profoundly disagree about basic ethical questions, like whether killing one person is somehow worse than merely letting someone die, and whether redirecting a threat is worse than introducing one de novo.²

But today I want to talk about an even more basic question—a question so fundamental that it’s presupposed by virtually everything written on the Trolley Problem.³ The question is whether “the numbers should count” in the ethics of rescue, whether one is morally obligated to give preference to the many just in virtue of their being numerous. In a nutshell:

Do you have to save a big group rather than a small one?

An alien encounter

For Philippa Foot—whose “Tram Driver” case got the Trolley Problem rolling—the question of numbers was so obvious that she didn’t bother to ask it.

We are about to give a patient who needs it to save his life a massive dose of a certain drug in short supply. There arrive, however, five other patients each of whom could be saved by one-fifth of that dose. We say with regret that we cannot spare our whole supply of the drug for a single patient, just as we should say that we could not spare the whole resources of a ward for one dangerously ill individual when ambulances arrive bringing in victims of a multiple crash. We feel bound to let one man die rather than many if that is our only choice. (1967, p. 9)

In a short reply, Elizabeth Anscombe said she felt a “curious disagreement.” In her view, saving the one would be perfectly permissible, since nobody among the five has a claim to be saved rather than the one, and five claims don’t add up to one big super-claim. (“Why not?”, one wonders.)

A decade later, John M. Taurek published “Should the Numbers Count?”—the first full-length defense of saving the few. Reading Taurek’s paper is, for many philosophers, a bit like encountering alien life. Whereas most of us find it obvious that five deaths are worse than one—just as five hours of pain is worse than one hour of pain, and $5 is worth more than $1—Taurek finds it equally obvious that pains and deaths and losses do not add up in any significant way.

This is a striking stalemate. If we want to resolve it, we’ll need something more than raw intuitions. We’ll need an argument. And it seems like exactly the sort of issue that ought to be resolvable through reasoned argumentation. This is a basic, simple moral question we’re talking about. It’s exactly up the alley of every moral theory. If ethics can’t answer the question of numbers, we have to wonder what it can answer.

As you might expect, plenty of arguments have emerged on both sides of this issue. Taurek has two arguments of his own. (See also Tyler Doggett’s work.) The number-counters have published dozens of pieces attacking Taurek from every angle you can imagine.⁴

But the most influential arguments have one thing in common: equality.

“Innumerate Ethics”

The most influential attack on Taurek came from Derek Parfit, whose “Innumerate Ethics” discredited Taurek for years in the eyes of much of the profession.

To Parfit, this wasn’t a scholarly back and forth. This was life or death. Taurek’s views were nothing short of a moral catastrophe, and if taken seriously, they could lead to policies that would massively increase the amount of death and pain in the world. Taurek’s “innumeracy” had to be contained.

For background on Parfit (and “Innumerate Ethics”), I recommend David Edmonds’ outstanding biography.

The peak of the critque comes in the very last section of “Innumerate Ethics.”

Taurek ends with this remark. Suppose we save the larger number. This would not “reflect an equal concern for the survival of each.” It would be like giving priority to saving the rich (pp. 3I5-3I6).

This is not so. If we give the rich priority, we do not give equal weight to saving each. Why do we save the larger number? Because we do give equal weight to saving each. Each counts for one. That is why more count for more.

That Parthian shot—Each counts for one, therefore more count for more—has become the most influential and widely repeated argument against Taurek. (Besides the classic “He’s crazy!”) The idea is that if your theory puts saving one on par with saving five, then it must be treating the one life as if it were more important—five times as important, one wants to say. That’s not equality: that’s partiality.

The ideal of impartiality that Parfit so eloquently invokes has its roots in the utilitarian tradition. “Each counts for one” is the telephone version of Jeremy Bentham’s “each tells for one,” where “tells” morphed to “counts” through the telling of J.S. Mill and Henry Sidgwick.

But it’s not just the utilitarians who use equality as a blunt weapon against Taurek. The great deontologists Frances Kamm and Tim Scanlon both make essentially the same argument.

Suppose Al, Betty, and Carol are in danger, and you can save either Al or Betty. It would be permissible, on nearly any view, to save Al.⁵ But now suppose you can save both Betty and Carol. Would it still be okay to save Al? Kamm and Scanlon say no. Adding Carol to the scales ought to make a difference. If it doesn’t, then her life is being treated as if it didn’t have any moral weight—that is to say, she’s being treated as less valuable, thus violating the ideal of equality.

Nor is it just Kamm and Scanlon who echo Parfit. It’s a lot of other ethics big shots (Raz, Setiya, Dougherty…). The leap from “Each counts for one” to “More count for more” can even be found in papers about moral codes for lawyers, and for how to distribute ventilators in a pandemic. Everybody, it seems, agrees with Parfit.

This is where I come in. In “Each Counts for One,” published last year in Philosophical Studies, I argue that Parfit’s inference is straight up logically invalid. “Each counts for one” does not imply “more count for more.”

“Each Counts for One”

Here’s the core idea of the argument.

Parfit and Taurek both say that equality entails their view. But I think they’re both wrong. Equality by itself doesn’t entail anything about whether the numbers count!

To see why, let’s break down Parfit’s view into axioms.

The trick here is to see that number counting in rescue cases is analogous to majority rule, which says that A beats B in an election iff more people prefer A. By analogy, number counters think that saving Group A rather than Group B is obligatory iff more people belong to A.⁶ The people’s interests have an influence on our moral obligations that is analogous to how voters’ preferences have an influence on an election.

Majority rule, conveniently for us, was axiomatized in the 1950s by the economist Kenneth May. (Easily in my top two Kens of 1950s social choice theory.) May proved that majority rule is the one and only rule that combines votes in a way that validates the following four axioms:

• Anonymity: no voter gets special influence

• Neutrality: no candidate gets special treatment.

• Positive Responsiveness: any vote added for A (or subtracted from B) will break a tie between A and B—in A’s favor, of course.

• Decisiveness: given everyone’s preferences, the rule will always say who wins (or else declare a tie).

By analogy, number counting is uniquely characterized by exactly similar axioms. Just replace “voters” with people in danger, “candidates” with outcomes that could be brought about, “votes” with lives at stake, and instead of thinking of who beats whom, the question is which outcomes must be chosen over which.

I think it’s clear that Anonymity—as an ethical axiom—ensures that the number counter values everybody equally. Thanks to Anonymity, nobody’s life is allowed to have extra influence on what’s obligatory. When we count up the number of lives at stake, we’re not allowed to say that Betty’s life counts for double, or that Al’s has infinite weight. Each counts for one! (No wonder May also calls his axiom “egalitarianism.”)

But notice that Taurek’s view is also in line with Anonymity, since it’s akin to unanimity rule, which gives each voter the same absolute veto power. Taurek’s rule, by analogy, lets anybody’s life act as a “veto” on the obligation to save a bigger group instead. Thus you may save Al rather than saving Betty and Carol. (Indeed, you may save Al rather than saving any arbitrarily large group of other people!)

The crucial thing to note here is that Taurek isn’t being partial to Al, here. You could also permissibly save Betty instead of any number of others, or Carol instead of any number of others, and so on. That’s what it means for Taurek’s view to be anonymous—and why I think it, too, lets each person count for one.

The really crucial difference between Taurek’s view and Parfit’s view isn’t that one is more egalitarian than the other—it’s that only Parfit’s view is Positively Responsive. This is where the action really lies. And, to be clear, I’m very keen to hear arguments for Positive Responsiveness. But we can’t argue for this axiom on the basis of equality. As the very existence of Taurek’s view shows, Anonymity does not entail Positive Responsiveness. And given that Anonymity is the real key to equality, we can conclude that equality doesn’t entail Positive Responsiveness, either. This is, in essence, why we can’t infer from “Each counts for one” to “More count for more.”

Coda

In the rest of “Each Counts for One,” I sift through a bunch of other arguments from equality to number counting, and in each case, I try to show how Taurek could coherently resist them.

This raises an intriguing question. Is there any argument that might break the stalemate between Taurek and Parfit? If not, then the question of whether the numbers count is ethically fundamental. In fact, that’s exactly what I think it is!

Conjecture: there is no convincing argument for, or against, the view that the numbers count—there is only a clash of basic intuitions.

I think this is a disturbing conjecture. Often we like to pitch ethics classes as a way to break through the stalemate of intuitions that emerge from “Trolley Problems” and real-world dilemmas. But if this conjecture is right, then there are shockingly basic limits on what ethical arguments can demonstrate. Instead of proofs and derivations, we’re mostly stuck with more or less refined judgment calls.

That is, unless someone else can come up with a clever argument where I couldn’t.

1. The point of Footbridge is rather oddly shrouded in mystery. Nowadays, people use the case to illustrate that it’s often wrong to kill one to save five. But that’s not how Judith Jarvis Thomson originally used it, either in her 1976 paper or her 1985 follow-up.

2. I’m blown away by how much good stuff has been written about the Trolley Problem in the last couple of decades, despite rumors of its having been beaten to death. Several favorites:

• Thomas Byrne, “The Bystander Doesn’t Kill” (from his MIT dissertation)

• Caspar Hare, “Should We Wish Well to All?” (Phil Review)

• Kieran Setiya, “Must Consequentialists Kill?” (JPhil)

• Richard Yetter Chappell, “Preference and Prevention” (F&E)

The all-time champion of Trolleyology has to be Frances Kamm, whose Trolley Problem Mysteries and Intricate Ethics are both masterful. (TPM also features some superb pieces from other philosophers. The Judy Thomson piece struck me as weirdly mean and obtuse. But the contributions from Shelly Kagan and Tom Hurka are worth your time, for sure.)

3. One exception is Frances Kamm’s “Aggregation and Two Moral Methods” from 2005. It’s not for the faint of heart, but the section on the Trolley Problem is extremely clear and forceful.

4. IMO, the most plausible line of attack on Taurek is that his view requires us to violate at least one of the following principles of “rational consistency”: transitivity, completeness, and context-insensitivity. I talk about transitivity and context in “The Many, the Few, and the Nature of Value.” I’m still figuring out my thoughts on completeness. (See Dorr, Nebel, and Zuehl’s paper for a recent defense of completeness. I’d also recommend Johan Gustafsson’s book on money-pump arguments.)

5. Exception: views with stringent requirements of fairness might require you to flip a coin. (Note that Taurek himself doesn’t have this view, though it’s weirdly commonly attributed to him.)

6. I’m speaking a bit loosely here—see the paper for details.

If you’re eager for complexity now, here’s a bit about two ways to spell out majority rule. “Simple majority rule” says A beats B iff A is preferred by more people than B is. “Absolute majority rule” says A beats B iff A is preferred by a majority of people.