Alt Binaries

I want to talk about a problem that everyone notices and almost nobody names, which is that democracy sucks at one specific job and is irreplaceable at another, and the two jobs are constantly being confused for each other.

Here’s the setup. There are five hundred people in a town. One of them owns the factory upriver. The factory dumps something orange into the water that smells like a dentist’s office on fire. The owner makes ten million dollars a year from the factory. The other four hundred and ninety-nine people each lose, let’s say, three hundred bucks a year in property values and an undefined amount of life expectancy from drinking the orange.

One vote per person, majority rules: the factory closes Tuesday. The owner goes from ten million to zero. The town goes from drinking orange water to drinking regular water and saving three hundred dollars each. Total welfare goes up. Utilitarian calculus says great, that’s exactly what democracy is for, glad we have it.

Now run the exact same math the other direction. Four hundred and ninety-nine people would each like, very mildly, to take a thousand dollars from the factory owner and split it among themselves. The factory owner would, very intensely, like to keep his money. One vote per person, majority rules: the factory owner is now poor. Total welfare also goes up, by the same math. Same democracy, same vote, same logic, totally different vibe.

The trouble is that the second story is also the first story. They’re literally the same arithmetic. There is no clean rule that separates “the majority correctly defending itself from a predatory minority” from “the majority correctly mugging a minority.” This is the binary I want to talk about today: intensity vs. breadth. The small group who cares a lot, against the large group who cares a little, and the unsolvable fact that whichever one wins, the other one gets bulldozed.

The whole edifice of “let’s just vote on it” runs on a hidden assumption, which is that one person’s preference is roughly the same size as another person’s preference. It isn’t. My desire for the parking lot to have one more space is not the same thing as your desire to not be deported. We pretend they are because we don’t have a unit of measurement. (Economists tried, they called it “willingness to pay,” and discovered to their delight that this means rich people have stronger preferences than poor people, which fixed everything.)

So you can side with breadth. Everyone gets a vote, count them up, the larger number wins, and if you’re in the smaller number on something you care about a lot (your religion, your house, your kid’s school), well, that’s the price of being outnumbered. Tyranny of the majority, people called this, back when phrases like that still moved units. It’s been kind of memory-holed because we’ve decided the only kind of tyranny that counts now is the other kind.

And the other kind is what you get if you side with intensity. You let the people who care most about a decision make the decision. This is how almost every functioning institution works, by the way. The HOA is run by the three people who will not shut up about the HOA. The school board is run by parents whose kids are at the school. The Federal Reserve is run by people who, alarmingly, find macroeconomics interesting.

Intensity scales down to the people who’ll actually do the work, and this is great, except that the people who care the most about an industry are the people in the industry, and what they care about, intensely, is making more money from the industry. (See: every regulatory agency, ever.)

So you get a thing where intensity-rule means the cigarette lobby writes cigarette law and breadth-rule means whichever ethnic group is biggest gets to decide what the smaller ones can eat for breakfast. You don’t get to pick a third option. The third option is “have a smart constitutional democracy with a bunch of rights and procedural safeguards,” which is just intensity and breadth wearing a hat. Every interesting fight in American politics is about which axis a given decision sits on, and pretending otherwise is what professionals call “having a job in the editorial department.”

Anyway. Here’s the long version.

Let me walk you through this from the ground up, because the standard treatments rush past what’s actually weird about this problem.

We already, intuitively, accept that intensity matters. Five votes aren’t always five votes when one of the voters is allergic to the thing on offer and the other four are mildly curious. The fact that one option strongly inconveniences a minority while the other only mildly inconveniences a majority should count, and we know it should count.

The problem is what happens when this scales up and the stakes get fuzzier.

But almost no real decisions distribute stakes evenly. Real decisions distribute costs and benefits unevenly, and that uneven distribution is usually the entire reason the decision exists. Nobody proposes a law that affects everyone equally; they propose laws to take something from group A and give it to group B, or to prevent group A from doing a thing to group B, or to require group A to pay for something group B wants. The whole point of legislation is that someone wins and someone loses.

And once you accept that, vote-counting becomes a deeply weird way to settle anything. The breadth side of the binary, in its purest form, says: we will use a tool that we know systematically miscounts stakes, because the alternative is letting some people’s stakes count for more than others, and that’s worse.

It’s a real argument. The strong version of it goes: yes, sometimes the majority will roll over a deeply-invested minority, and that’s a tragedy. But every other rule for weighing intensity has been gamed beyond recognition every time it’s been tried. The Senate is supposed to weigh intensity (small states with intense interests get representation disproportionate to their population). It currently functions to let a tiny number of voters in Wyoming and the Dakotas veto whatever a much larger number of voters in California want. The intensity in question is just the intensity of living somewhere with cheap land. An arbitrary minority gets permanent veto power because they happen to live in low-density places.

The courts are supposed to weigh intensity (they’re meant to protect minorities from majoritarian abuse via the Bill of Rights). They currently function as a venue where whichever team has appointed more judges in the last forty years gets to overrule whichever team won the last election. The Senate problem repeats itself in a black robe. An arbitrary subset of past elected officials, frozen in place, vetoes the current ones.

So the breadth case is essentially: every clever mechanism we’ve come up with to weight intensity has degraded into a power-laundering scheme for some specific entrenched group, and at least counting heads is hard to game. (You can game it by changing who counts as a head, but you can usually see when that’s being done.)

Then there’s the intensity side, which has its own pure form. The argument goes: a decision belongs to the people who will live with it. If the decision is about closing a school, it belongs to the families with kids in the school, not the people who pass it on their commute. If the decision is about a zoning change, it belongs to the people on the street, not the people across town. If the decision is about how an industry is regulated, it belongs to the people in the industry, because they’re the ones who’ll actually feel the consequences.

The intensity case is also a real argument. The strong version: democracy via one-person-one-vote turns every issue into a popularity contest among people who, statistically, know nothing about the issue and will spend less than two minutes thinking about it. This produces governance by vibes. Whoever can manufacture the most resonant feeling in the broadest population wins. The actual content of decisions becomes secondary to whether they sound good to people who aren’t paying attention. (This is, in case you haven’t noticed, the entire current political situation, in basically every democracy on earth, simultaneously.)

And the alternative (letting people who actually care about a topic make the decisions about that topic) sounds reasonable until you remember that the people who care most about an industry are the people profiting from the industry. This is what regulatory capture is. The FDA staffed by former pharma execs. The FCC staffed by former cable lobbyists. The Federal Reserve staffed by people whose entire professional class benefits from a particular set of monetary policies.

These aren’t conspiracies. These are the predictable result of taking the intensity argument seriously: let the people who care most run the show. The people who care most about Wall Street regulation are people on Wall Street. The people who care most about prison policy are prison guards’ unions. Whoever cares most has, by definition, the most skin in the game, and skin in the game is just another way of saying “personal financial interest in the outcome.”

So intensity gives you capture. Breadth gives you mob rule. These aren’t pathologies you can fix with better procedure. These are the two failure modes baked into the geometry of the problem. There is no third option that doesn’t reduce to one of these two with extra steps.

Now, here’s where it gets interesting. Most people are situational. They believe in breadth for issues where they’re in the majority and intensity for issues where they’re in the minority. Gun rights advocates believe in intensity (the few who care a lot should win) until the question is gun control polling, at which point they discover breadth (most Americans actually love guns, allegedly). Climate activists believe in intensity (the people who understand this care a lot, and that should matter) until they’re polling whether Americans want green policy, at which point they discover breadth. Everyone does this. Including, definitely, including me.

There’s a slightly cleaner version of this, where you say: “intensity rules for issues that primarily affect a small group, breadth rules for issues that affect everyone.” This sounds great until you realize that which category an issue belongs to is itself the most contested political question.

Is abortion an issue that primarily affects pregnant people (intensity) or an issue that affects the whole society’s moral character (breadth)? Is school curriculum an issue that primarily affects students and their families (intensity) or an issue that shapes the next generation of citizens (breadth)? Every actual political fight has, embedded in it, a meta-fight about which axis it sits on. The substantive disagreement and the axis-disagreement are inseparable, because picking an axis is mostly how you win.

One more thing. There’s a really popular pattern where people who lose on breadth try to relocate the fight to intensity, and vice versa. You lose a national election, you discover the importance of states’ rights. (Intensity: the people who care most about Texas should run Texas.) You win a national election, you discover the importance of federal supremacy. (Breadth: we all live under the same constitution.) Then your opponents lose and the polarity flips and now they are the states’ rights people. This happens within decades, sometimes within years, almost always within the same person’s lifetime, and the person almost never notices.

The deeper question, the one almost nobody asks: is there even a fact of the matter about whose preferences should count more? When the factory owner intensely wants to keep his factory and the four-hundred-ninety-nine townsfolk mildly want him to stop dumping orange dye in the river, is there a true answer to who’s right? Or is the answer just whichever procedure we ran?

The honest answer, I think, is that we don’t actually have access to comparing one person’s preferences to another’s. We made up a system where we pretend everyone’s preferences are the same size, because the alternative was a system where some people’s preferences obviously counted for more and that was Aristocracy and we were against it. The pretense is useful. It might even be necessary. But every so often it produces a result that’s so obviously wrong that we have to invent some side mechanism (courts, vetoes, constitutional rights) to override it. And the override mechanisms then become the new venue for the same fight, just at a higher level of abstraction.

This is why the question of democratic reform is, I’d argue, basically unresolvable. Every reform proposal is just a different mixture of these two ingredients. Ranked choice voting weights intensity within breadth. Proportional representation does the same. Veto points weight intensity over breadth. Federalism creates parallel intensity zones within breadth. None of these dissolve the underlying tension. They just relocate it.

Now for some examples (places where this binary shows up that you maybe haven’t thought about):

• Open source software governance. A library has ten million users and three maintainers. The maintainers want to make a breaking change. They care immensely. The users barely know the library exists, until the day their code breaks. Who decides? The maintainers, intensely involved, win every time, because the users have no mechanism to weigh in until it’s already too late. Open source is permanent intensity rule, which is why every popular library has a story of an unhappy fork.
• Casting in fan-favorite franchises. A studio is making a new Star Wars or Marvel movie. There are six million casual viewers who’ll see it once and six hundred thousand obsessive fans who will dissect every casting decision for months. The obsessive fans have intensity. The casual viewers have breadth. Studios that listen to intensity make movies for the fanbase and lose the general audience. Studios that listen to breadth make movies for everyone and the fans riot. The Star Wars sequels are, in a real sense, an academic case study of this problem.
• Bedtime, in any household with a small child. The child intensely does not want to go to bed. The two parents mildly want the child to go to bed. The two parents outnumber the one child. Intensity loses every night, and the child’s reaction (the screaming, the resistance, the elaborate stalling) is in some sense a coherent protest against a flawed voting system.
• Workplace coffee selection. Forty people in an office. Two of them care a lot about good coffee; the other thirty-eight will drink anything. The expensive coffee gets bought, because intensity wins quiet workplace battles. Compare to: the same office voting on whether to switch to a new accounting software. Forty people, two of them in accounting, thirty-eight who don’t care. Intensity wins again. Intensity wins most office decisions, which is why most offices are governed by their most opinionated employees rather than their headcount. (This is a feature when the opinionated person is right and a horror when they’re not.)
• Tabletop RPG group composition. Five players. One wants a horror campaign with permanent character death. The other four want a heroic adventure with low stakes. By breadth, the four win. By intensity, the one wins, because the four mild preferences can be accommodated within a horror game (lots of heroic adventures contain stakes) but the one intense preference cannot be accommodated within a heroic game (no stakes means no horror). Good DMs intuit this and run intensity. Bad DMs run breadth and produce campaigns where nobody quite gets what they wanted.

And now, having said all that, I will stop trying to be clear, because the topic is not actually clear, and the bit of it that isn’t clear is the bit that matters.

Consider that the entire dispute presupposes something we should perhaps not be presupposing, which is that preferences are the thing politics is for. Ask the man in the village in the steppes about the pipeline under his soil and what comes back is something other than a preference. He’ll tell you about his grandfather, about the goats, about a story from when the world was younger. The mother asked about the new school curriculum will tell you about her child. These are not opinions ranked among other opinions on a sliding scale. These are the substance of her actual life, which the polling apparatus then converts into a checkbox and counts.

To call these things preferences, and to add them up against the preferences of the petroleum executive in Houston and the school board member in the suburb, is to perform an alchemy that the Cappadocians would have recognised as devilry: the conversion of incommensurable things into a single fungible substance, so that they can be weighed against each other on a scale that does not exist. Bentham was the heresiarch who taught us this. We have been doing it ever since and we no longer remember we are doing it. Every count of votes is a small forgetting.

Read Aristotle on the polis and you find a man for whom this problem does not arise, because the polis was not the kind of thing that takes preferences as input. The polis was the medium in which a particular kind of human being (the politikon zoon, the political animal) came into existence at all. You do not vote in the polis to register what you want. You vote because the activity of voting, of speaking in the assembly, of being seen and heard by your fellows, is the activity through which you become a citizen rather than a slave or a beast.

Nobody in the polis is keeping score in the terms that would let a minority feel crushed by a majority. The fight is over what kind of city the city is going to be, and the losing side has been improved by the having of the fight.

We have lost this completely. We did not lose it gradually. We lost it on a specific day, somewhere around the publication of Mill’s Utilitarianism, when a clever man explained to us that political decisions are arithmetic problems about pleasure and pain, and we, the wretched descendants of Athens and Rome and Florence, said yes, that sounds about right, please continue.

The Albigensians believed that this world had been made by a lesser god, a botched demiurge who could not get anything quite right and whose creation was therefore not to be redeemed but escaped. Whenever I read a polling memo I feel myself growing slightly Albigensian. Here, in the orange numbers, is the demiurge’s own handwriting. Forty-two per cent of likely voters in the suburbs prefer outcome B. The minority intensity score is eleven points. The crosstab for the over-sixties shows a soft lean. This is what we have made of the political. This is what the heir of Pericles looks like now: a man in a cubicle in Virginia, weighing the preferences of strangers who have never met him and will never meet each other, so that a campaign manager somewhere can decide which colour of lie to tell next week.

I do not say this to lament. Lamentation is for people who think they could have done otherwise. We could not have done otherwise. The polis required a slave economy and a city of forty thousand and a religion that took the gods seriously and a thousand other conditions that we are not going to reassemble in our lifetimes or anyone’s. The choice between intensity and breadth is not a choice that the Athenians had to make, because the very thing that produced the choice (the assumption that politics is a clearinghouse for the satisfaction of individual desires) was unavailable to them. We have it because we are us. We are us because we have it. There is no exit.

But within the trap, watch what happens. The intensity people will accuse the breadth people of being unfeeling number-crunchers who would let a child drown if the polling went the wrong way. The breadth people will accuse the intensity people of being aristocrats in disguise, secretly believing that their feelings count for more than the feelings of the great unwashed. Both accusations are correct. Both groups are doing exactly what they are accused of.

The intensity people do think their feelings count for more, because their feelings are more, and that is the entire content of the position. The breadth people do believe in a kind of moral arithmetic that flattens the lived texture of grief and rage and devotion into commensurable counters. There is no honest version of either side that does not commit the sin the other side is pointing at.

The honest version of you is the one that knows you are doing the thing, and goes on doing it anyway, because the alternative would be doing the other thing, and you have read enough history to know how that ends.

Burton, in the Anatomy, observes somewhere in his thousand pages that the melancholy man is the one who has seen too much of both sides to commit to either, and who therefore wanders his garden talking to himself while the world is decided by lesser men. This is the actual fate of anyone who reads carefully on this question. You arrive at the position that intensity is correct in cases A through M and breadth is correct in cases N through Z, and then you discover that whether any given case is an A-through-M case or an N-through-Z case is itself the question being decided, and you go to bed.

There is an old engraving I keep seeing in my mind. I think it’s Bruegel, though I have not been able to find it again and am beginning to suspect I imagined it. Two crowds face each other across a market square. The larger crowd is enormous, hundreds, maybe thousands, all of them slightly bored, leaning on their pikes, looking off-frame at something more interesting. The smaller crowd is six men, all of them weeping, one of them on his knees, his hands raised to the sky.

In the centre of the square is a hole where a building used to be. The engraving does not tell you what the building was, or who tore it down, or whether the larger crowd is celebrating or merely standing there because that is where crowds stand. The grief of the six is given, in the engraving’s geometry, the same weight as the indifference of the multitude.

The engraver was on neither side. The engraver was the engraver. The engraver could see them both, and so the engraver could not help them, and so the engraver could only draw.

This is the position. There are six people weeping and a thousand people leaning on their pikes. You can vote, and the thousand will win. You can change the rules, and the six will win, and a different six will start weeping somewhere else. You can refuse to play, and the game will play without you.

The honest answer is not a procedure. The honest answer is that you have been given a tool that does one job badly and another job indispensably, and the job it does indispensably is the only one anyone has ever invented, and the job it does badly is the one you spend your whole adult life trying to fix, and you will not fix it, and you cannot stop trying.

So you go to the meeting. You vote. You lose, or you win, and both feel slightly wrong. You go home. The orange water is still running in the river. The factory is still there, or it isn’t. Somewhere a child is being told it is time for bed. Somewhere two men are arguing about a coffee machine. Somewhere a campaign manager in Virginia is reading a crosstab. Somewhere the engraver is putting down his tools, because the light is going, and the figures in the square will have to weep, and lean, and stand, until the morning, and after the morning, and after every morning, for as long as there are squares.

A small argument

KERRY: I’m just saying. There’s five of us. Three want pepperoni. Two want the white pizza with the truffle oil. Pepperoni wins. This is, like, a solved problem.

SIDONEI: Wonderful. A perfect little assembly of the damned. Let us all stand and salute the principle by which Galit and I, who have palates, are to be sacrificed to the geometric majority composed of you, your sister, and Vyacheslav, whose tongue I have personally watched accept pineapple chunks dipped in barbecue sauce. Yes. By all means. Run the numbers.

GALIT: I want to be clear that I would rather eat a candle than another pepperoni pizza from that place. The grease has its own postal address. It receives mail.

KERRY: Okay but that’s your problem. You have, what, a delicate stomach now? You used to eat…

GALIT: Don’t.

KERRY: …pizza off the floor in college. Literally. There was a slice on the carpet for like four days and you…

GALIT: I will fight you in this restaurant.

SIDONEI: The point, Kerry, has nothing to do with whether Galit has a refined palate or a betrayed one. The point is the shape of the decision. You are proposing a procedure in which the suffering of two is weighed equally against the very mild preference of three. You and your sister could eat almost anything. Vyacheslav could eat a tire. We are being held hostage by the indifference of people who claim to be voting.

KERRY: “Held hostage.” It’s pizza.

SIDONEI: Every tyranny in human history has begun with someone saying “it’s only pizza.”

GALIT: That’s true, actually. The Albigensian Crusade started over a calzone.

KERRY: Please stop helping him. Listen. Listen. If we let the intensity of preference decide everything, we’ve stopped being a group and started being a hostage situation. Every time we eat together, the person who’s most upset about the options wins. Which means the person who learns to perform being most upset wins. Which means we’re picking dinner based on theater. Vyacheslav, are you with me on this one, buddy?

VYACHESLAV: I really am okay with anything.

KERRY: See? That’s a man at peace with the world.

SIDONEI: That is a man whose palate was destroyed in childhood and who now consumes calories purely as a chemical exercise. He attends our dinners the way weather attends a picnic.

VYACHESLAV: I want to register that I find that hurtful.

SIDONEI: Oh good, Vyacheslav has registered a preference. The temperature in the room has dropped two degrees. Quickly, everyone, gather round and weigh his feelings against my actual gustatory destruction. Let us tally.

KERRY: Here’s what’s actually happening. You and Galit have a strong preference. Fine. So what you’re saying is your strong preference should override our majority. Okay. Now imagine…

GALIT: Here we go.

KERRY: …that next week, Vyacheslav decides he really really really wants ramen. Stronger than any preference any of us has ever had. He has a vision board for it. He has, like, ramen-related grief. Do we eat ramen?

SIDONEI: Naturally. If Vyacheslav has been so transformed by life that he develops a genuine preference, we should honour the historic occasion. We should declare a feast day.

GALIT: The Feast of Saint Vyacheslav, Patron of First Opinions.

VYACHESLAV: You two are being so mean tonight.

KERRY: You’re dodging the question. Imagine Vyacheslav’s hypothetical ramen preference is real. Strong. Genuine. Three of us, however, do not want ramen. We want, I don’t know, tacos. Tacos for three of us. Ramen for him. Does he win?

SIDONEI: Hmm. Hmm. Now this is where you have me. Because, you see, his preference is intense, and ours is moderate, and by the principle I have been articulating…

GALIT: Tacos. We get tacos.

SIDONEI: Yes. Tacos. Obviously tacos.

KERRY: So intensity only counts when it’s your intensity. Got it. Cool. Cool cool cool.

SIDONEI: Listen. Listen carefully. There is no doctrine here. There is only the question of which procedure produces the best dinner. In our specific case, with these specific people, ordering this specific pizza, the right answer is the white pizza with truffle oil, and the reason it is the right answer is that Galit and I would be miserable for the rest of the evening if we did not get it, and you three would be slightly less excited but functionally fine. That is the calculation. I have no theory to defend. I have a meal to order.

KERRY: That’s just… that’s just saying we should do whatever you want.

SIDONEI: No, no. That is what it sounds like to a person who has not been paying attention. What I am proposing is that we recognise the difference between a vote that registers a fact about who cares, and a vote that pretends everyone cares equally so that the people who care most can be safely ignored. The first is a tool for finding the answer. The second is a tool for evading it.

VYACHESLAV: Could we get two pizzas?

(Long silence.)

KERRY: Vyacheslav, my brother in Christ. We have been arguing for twenty minutes.

SIDONEI: About the geometry of human preference.

GALIT: About the soul of democracy itself.

VYACHESLAV: Yeah. So two pizzas?

KERRY: …we should get two pizzas.

SIDONEI: Vyacheslav has solved Athenian democracy. Someone get him a medal.

VYACHESLAV: I would prefer a piece of pizza.

Further reading

• Alt Binaries home (the full archive of binaries, in case you want more