Pigeons, Jan Tinbergen and A Scott Sumner Post
The Pigeonhole Principle
Every summer, I spend a month in the lovely town of Manipal. We hold a summer camp there that is very close to my heart, and this summer will be no different.
It is a lovely way to spend the summer: kids with insatiable curiosity, taught by faculty with inexhaustible enthusiasm over three weeks. No exams at the end of the process, so students choose to learn the subject for the love of it. Glorious, just glorious.
It helps that Manipal has some of the best dosas and fish curries India has to offer, and I’ve had many meals with the folks who come to teach at the camp, where the quality of the victuals on the table are in an extremely close race with the quality of the conversation around it.
And one such conversation over one such meal helped me learn about the pigeonhole principle. It is an extremely simple idea, the pigeonhole principle. So simple that I can tell you about it in one short sentence, like so:
The Pigeonhole Principle states that if n items (pigeons) are placed into m containers (pigeonholes), and n>m, then at least one container must contain more than one item.
Save your smart-aleck responses, people, and I tell you this from first-hand experience. “Ah-ha!”, you might be tempted to say, “now that’s a surprise!”. Or some such smug little line. But, as I say, desist. Because the point isn’t about how simple the principle is, but rather about how sophisticated its applications are. Here, knock yourself out.
That’s the first of the three pillars that make up this post. Now let us go meet the second.
The Tinbergen Rule
Every econ student meets the Tinbergen Rule, sooner or later.
It is named after Jan Tinbergen, a Dutch economist from a while back. Useful pub trivia: he won the first Nobel Prize in economics. And an inside reference for students of economics everywhere: he’s also considered to be one of the fathers of econometrics. So if you find yourself staring balefully at Damodar’s book at two in the morning, you know whom to blame. Partially to blame, of course - we’re talking about a multivariate model here.
But anyway, back to the Tinbergen Rule:
In his work on macroeconomic modelling and economic policy making, Tinbergen classified some economic quantities as targets and others as instruments. Targets are those macroeconomic variables the policy maker wishes to influence, whereas instruments are the variables that the policy maker can control directly. Tinbergen emphasized that achieving the desired values of a certain number of targets requires the policy maker to control an equal number of instruments. This is known as the Tinbergen Rule.
I hope you’ve made the connection, because conceptually speaking, it is an obvious one. The Tinbergen Rule is a restatement of the pigeonhole principle. Mathematicians at certain dinner tables in Manipal have been known to snort derisively upon hearing of the Tinbergen Rule, and they would have expressed themselves more fully too, had the pomfret not been just that good on that particular day.
That’s the second pillar of our blogpost. Which brings us to the Scott Sumner post.
Conflict and Competence
That’s the title of Scott Sumner’s post from today, and while you should read the whole thing, here is a useful excerpt:
During the Chinese Cultural Revolution (1966-76), students persecuted people that had relatively high levels of education. Many professionals were sent to the countryside and roughly a million people died (500,000 to 2 million—no one knows the exact figure.) In the Chinese film To Live (1994), there is a heartbreaking scene where the formerly arrogant students realize that they need experts to help them out. Here’s how Wikipedia describes the scene:
Months later, during Fengxia’s childbirth, her parents and husband accompany her to the county hospital. All doctors have been sent to do hard labor for being over educated, and the students are left as the only ones in charge after they have “overthrown” the doctors. Wan Erxi manages to find a doctor to oversee the birth, removing him from confinement, but he is very weak from starvation. Fugui purchases seven steamed buns (mantou) for him and the family decides to name the son Mantou, after the buns. Fengxia begins to hemorrhage, and the nurses panic, admitting that they do not know what to do. The family and nurses seek the advice of the doctor, but find that he has overeaten and is semiconscious. The family is helpless, and Fengxia dies.
Scott’s post argues that the same phenomenon can be observed in present-day America. The scene(s) from To Live, Scott says, are just a particularly extreme example of a much more general phenomenon, the war on competency by political fanatics.
Anybody who is not MAGA in America these days, Scott says, is not going to survive for long ‘in the Justice Department, the FBI, the intelligence agencies and the military’. And other places besides, I’m sure. But the phenomenon is the same as what happened to the doctors in China: you don’t conform, therefore you are bad.
Conformity, or belonging, or being a part of the “in” group is important. If you don’t conform, you don’t belong. If you don’t conform, you are bad.
Conformity is not just being used to assess ideological alignment. It is being used as a proxy for quality. If you don’t conform, you are by definition not good.
Two dimensions (n): conformity and quality. One metric for judging (m): conformity.
Two targets: conformity and quality. One instrument: conformity.
The pigeons are telling you the same thing that Jan and Scott did!
TMKK?
This isn’t about the right or the left. The communists did it in China, and MAGA is doing it in America. Neither is it about cultural values: Asians did it in China, and Americans are doing it in America. And no matter where in the world you are reading this, you can rest assured that folks in your country have done it in the past, are doing it now, and will do it in the future.
Worse, you have almost certainly done this yourself. All of us look for proxies for quality, and those proxies tend to be related to how ‘like us’ the person being evaluated is. And the more that person is ‘like us’, the better we assume that person to be.
Just like the AIs, us humans too have jagged frontiers. Voting for the same party, praying to the same god, having the same religion, or using the same agentic harness as us is no guarantee that the person being evaluated will be as good (or as bad) as we ourselves.
It didn’t work for China back then, it won’t work for America today, and it will not work anywhere in the world. Evaluating a person’s quality along a particular dimension isn’t the same as evaluating a person’s beliefs.
People will very quickly latch on to what is being evaluated, and will learn to optimize for being excellent along that one particular dimension. So if tomorrow we as a nation say that we will allow people to read blog posts based solely on the quality of the mohawk haircuts on the author’s heads, well, I’ll be paying a visit to Dr. Batra’s clinic.
Old time readers will recognize this for what it is: Goodhart’s Law. Goodhart’s Law says that a measure that becomes a target ceases to be a measure. If the measure of quality is ideological alignment, then people will optimize for pretending to have ideological alignment, quality be damned.
Take a look at the world around you, and you will realize that we’re all playing a game in which we try to guess what the current-day equivalent of top-notch mohawks is for our society. Again: this is true no matter who you are, and which country you are in… and it is true regardless of when you are reading this.
The point of this post?
Listen to what Jan, pigeons and Scott are telling you, and learn to look beyond the mohawks.
It matters.