Last time I ran the New York Times Spelling Bee through the machinery of cooperative game theory, treating each day’s word list as a weighted voting game: words are voters, points are votes, Genius is the quota, and a word has power when it’s the one that carries you across the line. The punchline was that the power ranking is boring — a rescaling of the scoreboard — until you replace the fiction that you find words in random order with a model of how people really solve, common words first.

The best way to kill a joke is to explain it. This is a series about explaining jokes. Each installment takes a game people enjoy and runs it through the machinery of cooperative game theory until the fun stops. The wager is that the autopsy is where the biology is — if you want to know how a game really works, it helps to ruin it first.

We came to Montreal for a talk — Maggie's, at a conference I'll get to next time — and I did what I always do in a city that predates the automobile, which is walk until my feet complain and then walk a little more. Old Montreal rewards the stubborn. The streets in the old quarter still run on their seventeenth-century logic, narrow and cobbled, tilting down toward the river, and on a bright afternoon the crowd thickens into that pleasant shuffle where nobody is quite going anywhere.

Thursday's post ended on a one-dimensional dial and a promise. The promise was that a single dimension is exactly what majority rule needs in order to behave. Turn an evaluation loose across many dimensions and it cycles — McKelvey and Schofield, the chaos in this blog's masthead1 — but compress the whole question of equitable-versus-uniform onto the lone parameter \(\kappa\), and the chaos has nowhere to start.

Wednesday's post answered what selects: a stationary distribution, the wheel turning by no hand in particular. Knowing what the dynamics pick, though, is not the same as knowing whether they picked well. So step off the graph — out of the local view every node is stuck inside — and try to do the one thing the nodes themselves never can: grade the result.

Last week I asked you to take your hand off the lever. The argument, compressed, was that the designer we kept reaching for — the planner who would tune the network so cooperation paid and nobody got fleeced — dissolves the moment you write him into the model. There is no seat at the controls. A few days in Tokyo did nothing to soften the conclusion, so I will let it stand.

TOKYO — Earlier this week I wrote that there was a man I meant to come back to before I left Japan. This is me keeping the promise. The meeting that Maggie and I came to Tokyo for is the gathering of the Society for Social Choice and Welfare, and at the turn of the century its president was Kotaro Suzumura, of Hitotsubashi University, across the city.

TOKYO — For most of this week I have been the one standing at the board. This morning I had the easier and far better job: a seat in the audience, watching a set of results I had not seen finished until they went up on the screen. The conference is the Society for Social Choice and Welfare, and the speaker was…

TOKYO — No guidebook leads with this, but Tokyo spent much of the twentieth century as one of the world's quiet capitals of a strange and beautiful science: the mathematics of collective choice, the study of what a group of people actually do when they try to decide something together. The founding puzzle is older than the United States Constitution. In 1785 the Marquis de Condorcet noticed that a room of perfectly reasonable people could vote themselves in a circle — a majority preferring A to B, another preferring B to C, and a third, maddeningly, preferring C back to A — and that the circle was no one's error but a standing property of majority rule itself.

UENO — Two kinds of time trouble follow me around, and only one of them is worth a paragraph. The first is jet lag, which is real, tedious, and has nothing to teach anybody: my body is keeping East Coast hours in a city that gave them up long ago, and it will right itself in a week the way it always does.

UENO — Two kinds of time trouble follow me around, and only one of them is worth a paragraph. The first is jet lag, which is real, tedious, and has nothing to teach anybody: my body is keeping East Coast hours in a city that gave them up long ago, and it will right itself in a week the way it always does.

A confession before we start: I billed this as three posts, and the arithmetic has not cooperated. The last two turned up a result and a question big enough that I'd rather run long than rush them, so the series will continue past today. This post is the third, and it is the hinge. Monday showed that imitation copies a strategy and silently inherits a seat; …

A confession before we start: I billed this as three posts, and the arithmetic has not cooperated. The last two turned up a result and a question big enough that I'd rather run long than rush them, so the series will continue past today. This post is the third, and it is the hinge. Monday showed that imitation copies a strategy and silently inherits a seat; …

On Monday I split the payoff an agent earns into a part that travels with the strategy and a part that stays with the seat, \(f_i = \alpha_{s_i} + \beta_i + \varepsilon_i\), and promised that the positional term \(\beta\) has a closed form that takes about three lines to derive. Today we derive it. The exercise is worth doing slowly, because it turns the paper's headline — that the rule which best spreads cooperation is also the rule that worsens inequality — from a surprising empirical finding into something closer to a definition, and because it exposes a question hiding inside an innocent word.

Uniform sharing of public goods can boost cooperation in social networks, but often concentrates benefits among well-connected individuals, creating inequality despite greater collective success.

When you face a decision you don't know how to make, you look sideways. You find someone who is doing well — the colleague who made tenure, the neighbor whose kids turned out kind, the friend who somehow retired comfortably a decade early — and you copy what they did. But the rule has a catch, easiest to feel at the limit.

"Should I put this in the junk drawer?" "I dunno. Do you think you could figure out where it goes?" That exchange is short enough to miss, and it is the entire subject of today's post. The first post in this series introduced the junk drawer as a load-bearing component of any well-designed classification system, home to the lost key (waiting on information that hasn't arrived) and the screwdriver (useful across categories, which is the point).

The Supreme Court has twenty-three cases left to decide this month, and one of them is Trump v. Cook. The facts, briefly: last August, the President posted a letter announcing the immediate removal of Federal Reserve Governor Lisa Cook, citing uninvestigated allegations that she misstated her residency on mortgage paperwork before she joined the Board. Cook declined to leave, on the theory that the Federal Reserve Act permits her removal only "for cause" and that an unproven allegation about a 2021 mortgage is not one.

A new paper by Alexandre Morozov and Alexander Feigel in PNAS offers a genuinely interesting evolutionary result. If each player in a population of Prisoner's Dilemma agents carries an opponent-indexed cooperation probability — \(p_{c,i\to j}\), one entry per partner identity — then selection and mutation routinely produce cooperative configurations. The press release framed this as resolving the Prisoner's Dilemma after seventy-five years of pessimism.

NANCY — A few days ago I promised a dispatch on the keynote, and here it is. The eighth International Conference in Philosophy and Economics met this week in Nancy, and the keynote was given by my closest collaborator, who is also my wife, Maggie Penn. Her title was “Three Paradoxes of Optimal Evaluation.” I sat in the back of the lecture hall and took notes like a correspondent (as the attendance, pictured below, suggests, Maggie gives a great talk).

NANCY — I have come up out of the tunnel, across France, and into Lorraine, to a conference on economics and philosophy, and the first thing worth saying about the host city is that it is the birthplace of the man who discovered that three of anything is trouble. Henri Poincaré was born here in 1854. The masthead of this blog has carried the words “Three Implies Chaos” since its first day, and this dispatch is filed, as it happens, from the place where the chaos was first found.

BENEATH THE ENGLISH CHANNEL — Having just reoriented myself to turning my head to the right when about to cross the street, I have boarded the train at St. Pancras with Maggie, as we leave London and head to the 8th Conference on Philosophy and Economics in Nancy, France --- via Paris, of course. There is a stretch of this journey, an hour or so out of London and deep beneath the seabed, where the phone signal dies and there is nothing to do but think about infrastructure.

LONDON — I came up out of the Underground this morning at the wrong station, a humbling way to begin a post about the meaning of position. The conference I am here for, the Warwick/Yale/Princeton meeting on political economy, takes its name, at one remove, from an English county whose old town lent its name to an earldom. I will get to the earldom.

Six posts since the last Dispatch, four of them a single arc on AI as a classification system. The arc started with a Vice President who could not evaluate her engineers, passed through a benchmark that turned out to be measuring string length, paused on a paper about elite athletes that was Berkson's paradox in a tracksuit, and ended at the moment an LLM put a three-item menu in front of me and waited for me to pick.

Earlier today, while I was working with an LLM on something, it asked me a question. Here is the question. Three options. They differ from each other in ways the menu makes plain — inherit the body's numbers and flag, correct everywhere, or correct the appendix and flag the body as wrong. The point of this post is not which one I should have picked.

A new paper in Science — Gullich et al., "Recent discoveries on the acquisition of the highest levels of human performance" — looked at top performers in athletics, science, math, and music. The headline finding is one most parents would like to hear: among the highest adult achievers, peak performance is negatively associated with early performance. Don't push your kid to specialize early; let them play in the yard.

While similarly post-apocalyptic and "numbers-driven," this post is not actually about a new NetFlix series. Rather, the main character of the story is HaluEval, a new "standard benchmark" for measuring whether a large language model is hallucinating — producing fluent, plausible-sounding text where it ought to be reporting a fact. The benchmark contains around 35,000 examples, each labeled as a hallucination or not.

When I introduced the junk drawer a few posts back, the example was a physical one. Most kitchens have a drawer that holds the screwdriver, the rubber bands, the takeout menus, the AAA batteries, and the one weird key nobody can identify. The drawer is not a failure of organization. It is the part of the organizational system that handles things which do not fit anywhere else — and, more importantly, things that would not fit any better if you tried to file them somewhere else.

There are no stupid questions… Dear NSQ, I grew up in Pittsburgh and learned to drive there. Last month I took a left turn from Tate Street onto West Market Street the way I always have — when the light turned green, I went, before the oncoming traffic could reach the intersection. The driver across from me laid on the horn for what felt like a full second, and so did the two drivers behind him.

A Vice President at a large technology company sits down at the end of the quarter to evaluate her engineering team. She has twelve direct reports. They have spent the quarter using AI tools heavily, as the company's leadership has insisted they do. She must now write performance reviews. She has to say, in writing, which engineers used the AI well and which did not.

Friday's post argued that what the Court did in Louisiana v. Callais is best described as breaking a structural link — a load-bearing connection that was holding up many actions at once, not just the Louisiana map. That post was about what. This post is about why now. Why this case, why this term, why — for that matter — thirteen years after…

Wednesday morning I posted “You Can Get There From Here, Or: The Theorem in the Tagline,” a piece I had been meaning to write for fourteen years. It is a short essay about why McKelvey-Schofield — the result that majority preference cycles can wander anywhere in the policy space once procedural constraints fall away — is the theorem the blog's tagline has always been pointing at.

Justice Kagan opens her Callais dissent with a hypothetical. She knows it's stylized, and she says so. Imagine a state shaped like a rectangle, with one of its six congressional districts a near-perfect circle in the middle. The circle is ninety percent Black. The other five districts, surrounding it, are ninety percent white. Voting is racially polarized. Black voters, concentrated in the circle, elect a representative of their choice.

The previous post used the phrase "local data" something like thirty times. The phrase did most of the heavy lifting in the argument: local data does not determine global structure, the more holes the underlying object has the more slack between local and global, and so on. I want to start this post by interrogating the phrase, because once you look at it carefully it turns out to be a beautiful piece of mathematical convention and to be doing far more work than the previous post gave it credit for.

The previous post used the phrase "local data" something like thirty times. The phrase did most of the heavy lifting in the argument: local data does not determine global structure, the more holes the underlying object has the more slack between local and global, and so on. I want to start this post by interrogating the phrase, because once you look at it carefully it turns out to be a beautiful piece of mathematical convention and to be doing far more work than the previous post gave it credit for.

This blog has been operating under the subtitle "Three Implies Chaos" since 2012. Long-time readers know the phrase pulls multiple duty: Li and Yorke's period-three theorem from chaotic dynamics, Arrow's theorem on preference aggregation, the Gibbard-Satterthwaite theorem on strategic manipulation, and the McKelvey-Schofield chaos theorem on multidimensional voting. Each of these results says, in its own register, that once three or more elements enter a system the system stops behaving the way the system was supposed to behave.

In 1867, the French mathematician Pierre Ossian Bonnet asked a question that sounds like it should have an obvious answer. If you know the metric of a compact surface at every point — the intrinsic distances and angles, the things you could measure if you were a tiny ant walking on the surface — and you also know the mean curvature at every point — the extent to which the surface is bending in the three-dimensional space it sits in — does that determine the surface?

Saturday night, Round 1, the Pittsburgh Steelers are on a video call with the wide receiver Makai Lemon. They hold pick 21. They are telling him, in front of cameras, that they intend to take him. Lemon, unflappable, accepts the news. Then his phone buzzes with another incoming call. The caller ID says Philadelphia. Why is Philly calling me? he asks, into a room of Pittsburgh personnel who are still on the line.

Five posts since the last Dispatch, organized as two arcs: Monday through Wednesday tracked the news in real time, Thursday and Friday returned to the methodological pieces those posts depended on. The tightest moment came Wednesday — the Iran prediction the April 17 post staked landed around 5pm, and the Virginia rule the Wednesday post analyzed got struck down by a court four hours later.

Roosevelt Elementary started Year 1 of Elevate with 100 students. It ended the year with 400. The other two schools held roughly steady. The district grew from 600 students to 900, and the composition of that denominator shifted decisively toward the lowest-scoring school. That one fact explains the entire dashboard. Elevate worked. Every school's average SAPA score went up three points.

Yesterday Virginia voters ratified a constitutional amendment giving the General Assembly temporary authority to redraw the state's congressional districts before 2031. Most of what you will read about the result over the next few days will concern seats — specifically, whether Virginia Democrats will in fact net four additional House seats in November under the pre-drawn map that House Bill 29 carries into effect.

Here is what today looks like. The ceasefire, which was originally set to expire Tuesday evening Eastern time, will now expire Wednesday evening Eastern time — the deadline has slipped by roughly twenty-four hours, which is about the time it takes to fly from Washington to Islamabad. Vice President Vance is reportedly departing today for Wednesday's talks. Iran has not confirmed attendance.

A quick correction on The Only Clause Available, published Friday. I wrote there that the US–Iran ceasefire expires Monday. It expires Wednesday, the 22nd — the two-week truce began April 8, and I miscounted by two days. (Ed.: A formal theorist, miscounting.) The prediction itself stands for Wednesday: a renegotiated form of ambiguity rather than either a settled deal or a clean resumption of hostilities.

A dispatch from the road, later than usual. The week covered the launch of the junk drawer series, a USPS post whose central mechanism acquired a fuel surcharge while the post was still fresh, a Supreme Court case in which the drawer breaks, and a Friday post on Iran that staked a prediction now counting down to Tuesday. Plus: a 213–214 vote, a reopened-then-reclosed strait, and a second ceasefire with its own clock.

Here are two statements about the same agreement, issued within twenty-four hours of each other, by officials who were present at its creation. Donald Trump, April 8, 2026: "There will be no enrichment of Uranium, and the United States will, working with Iran, dig up and remove all of the deeply buried Nuclear 'Dust.'" Iran's published 10-point proposal, same week: "acceptance of enrichment."

For more than a century, the constitutional status of religious exemptions from childhood vaccine mandates sat quietly unresolved. States offered exemptions — or didn't — as a matter of legislative discretion. No court had to rule on whether parental religious objection was a constitutional right or merely a policy option that legislators could extend or revoke. The ambiguity was functional: schools could plan, public health authorities could enforce mandates, and the system worked.

Monday's post introduced the junk drawer as a structural feature of any well-designed classification system — not a failure to be corrected, but a load-bearing component. It offered a typology: the lost key, which is in the drawer because it is waiting on information that hasn't arrived yet, and the screwdriver, which is in the drawer because its cross-category usefulness is precisely what makes it valuable.

Yesterday's post was about junk drawers — about what happens when you ask a classification system to sort an unruly world in real time, and about the organizational costs of pretending the system is tidier than it is. I had barely finished writing it when I came across a news story from two weeks ago that I had, somehow, missed. On March 31, the President signed an executive order giving the U.S.