You’ve just reached into a large opaque jar and pulled out the number 87. I could add some other structure, that the biggest number is 100, or that odd numbers are twice as common as even, and then ask clearly answerable questions. But what if we know nothing more than what we’ve seen: a ball from the jar with the number 87? What’s the biggest number in the jar? Are there even other numbers in the jar? Or you’ve reached in and pulled out a purple marble, how many colors of marble are there? Are they all round? Are there any numbers in the jar? Some of these have actual answers, and that’s important because they link to a bigger question:

What do our philosophies of statistics fill in about our world when they’ve seen almost nothing from it?

Or put another way: just how much can you know about the world with nearly no data and nearly no theory? I’m in social science, so it’s a real thrill when I find knowledge I can trust. And to do it from nearly nothing is astonishing. You can get the shape of the world from just 1 or even 0 observations. As an empirics-first person, I’m surprised to hear myself say it, but there’s so much you already know about the world when you don’t know nearly nothing. I’ve been collecting examples for year. And these examples have actually helped me do normal things, like find my keys, charge my phone, and, thanks to German tanks, take a long, hot shower.

The foggy sea, the German tank problem, and showers at a campsite.

You’ve been wandering for weeks, no map, through a foggy landscape. You reached a body of water, knowing nothing about how large it is, and decided to cross it with your inflatable raft. It’s been about 10 minutes already, so you know that this body of water is bigger than a creek, but it could be a lake, sea, or ocean. It could be another 2 minutes to the other side, or two months. Knowing nothing, what’s your best guess for the total size of the lake?

This is a continuous version of a famous statistical problem called the German tank problem. The Allies need to estimate German tank production. As they captured and examined German tank hulls, they found that their engines had serial numbers. So if you’ve captured a tank with the number 200 on the engine, you immediately know that there are at least 200 tanks. But does that also tell you anything about the total number of tanks? It does, and that’s fascinating: it’s a hint of everything you know when you know almost nothing.

And it’s not just a matter of theory. I was at a camping ground with spotty hot water. Some days there was as much as you want, and others it only lasted long enough to get your hopes up, just one minute or two, before getting icy. So if you’ve been in the shower for one minute, you know that there was at least one minute of hot water available, but do you now know anything about how much hot water is left?

Amazingly, you do. And that’s useful to know. If you need 10 minutes to wash your hair, you’ll be in a bind if the water goes icy in five. And absent the magic answer, it’s not entirely clear what you should do. Play it safe and never wash your hair? Roll the dice and have soap in your eyes when the water turns cold? Well there’s a solution to this problem, the German Tank Problem, and to the problem of the foggy sea: Your best guess at any moment is that you’re halfway through. So if you’ve been rowing for 10 minutes, then your best guess in this moment is that there are ten minutes of rowing. And every minute after that you best guess will go up (not down!). If you’ve captured tank #350 then your best guess in this moment is that there are another 350 tanks, for a total of 700. And if you don’t know if you’ll have five minutes of hot water in the shower, spend the first five minutes showering cautiously, as if the hot water could end at any moment. At the five minute mark you have a legitimate reason to feel confident that you’ll have five more minutes to wash your hair.

That’s what I did, and it worked!

Connection to science

The scientific method in the West comes out of several centuries of debate: can you know the world by reason alone? By observation alone? To skip past a lot of arguing, the answer is “both” via the scientific method, a procedure for bringing reason and observation into dialogue. But in practice they’re always in balance, and whether to center theory or data differs so much by discipline. In some areas of knowledge, like physics, data drapes beautifully off the framework of theory. In others, with phenomena that are too complex for elegant theories (e.g. social science), theory does a much more sorry job at propping up the data, so you end up using the data as its own model. that explains the role of machine theory, information theory, and statistics. As a social scientist your theories aren’t nearly good enough to really predict outcomes, and you spend a lot of time with statistics, the part of math that turns data into knowledge.

The conventional statistics that social scientists are taught can be called “small-n” statistics because it was developed in the early 20th century when it was costly to collect many independent observations (n represent your total number of observations). You had to squeeze every bit of insight from the couple dozen n you could get. The computing of the 21st century brought us big data and a switch to an alterantive philosophy of statistics that could leverage large n.

Within that frame, this exercise, “what you know when you know nothing” is a bit of a throwback. We drop from large-n statistics, down past small-n statistics, to the very smallest-n statistics of n=1.

Relevance to the philosophy of statistics

There isn’t just one statistics of n=1, and there’s actually a different answer to the German Tank problem. There are two alternative philosophies of statistics: the frequentist and Bayesian paradigms. There is a clear formal difference that is hard to cast intuitively, but narratively frequentism develops statistics by estimating what will happen from what has happened, while Bayesianism understands statistics as a problem of estimating what will happen from an observer’s beliefs about what has happened. Instead of trying to figure out how many tanks are in this world, the Bayesian observer imagines a range of possible worlds, in which the Germans have built everything from 2 to 20,000 tanks, and they work to determine which of those worlds we’re in. It may sound like a subtle distinction, but philosophically it’s big and mathematically it’s big. And, as we’ll see, the different philosophies predict very different numbers of tanks.

Between the two, Bayesianism is ascendant today because it wasn’t feasible to use before the ubiquity of cheap computing, but one isn’t better than the other. They are both ways of writing models, and all models are wrong.

One practical difference: the Bayesian approach is better for handling the complexity that comes with a lot of data, while the frequentist approach was developed for the era of “small-n” statistics, when the challenge was usually to learn as much as you could from very little data. And because the German Tank Problem is a “very very small data” problem, the frequentist answer is better. The frequentist answer is the one I’ve described, that what you’ve observed is half of the total. The Bayesian solution is that what you’ve observed is the total: if the largest serial number you’ve seen is #350, then your best guess is that there are only 350 tanks, because, assuming tanks are costly to produce, a world of 350 tanks is the one with the most evidence.

But the Bayesian way of thinking has it’s own place as well in revealing what we know when we know nothing.

How to find your keys

I lost my keys on the ride to the gym, somewhere on a mile-long stretch, and it was dark by the time I came out of the gym and realized it. I didn’t want to wait till morning, and I didn’t want to backtrack slowly and spend a half hour looking carefully. After all, they could have been anywhere. So I thought about it. Are my keys equally likely to be anywhere along the mile stretch? Or are they more likely to be in some places than others? I could be in a world in which it was very unlikely that I would lose my keys at all. In that world they really could be anywhere. I could also be in a world in which they were just waiting to be lost, as if they were scotch-taped to the outside of my side pocket. In that world I probably lost them right away, walking down my steps. I didn’t know which world I was in, or which of all the worlds in between, but in more of those worlds my keys were near my front door. So instead of searching slowly back home from the gym, I decided to ride straight home and start the search at my front door. My keys turned out to be right there. In most possible worlds, you lost your keys as soon as they were loseable, and they are most likely to be wherever you last remember having them or moving them. The power of Bayesian reasoning is that you can reason to that, and you can prove it too, which some friends helped me do in another post.

How much charge is on your phone?

If you look at your phone, it’s unlikely that it’s at 68% charge. But unless it’s constantly dead (0%), or constantly charging (100%), it is more likely to be at 68% than anything else. If you charge intermittently, but enough to stay above empty, and not enough to keep at full, then you can think of it this way: It’s morning and you’re at 100%. By evening it would be at 0%, but you charge in little moments during the day. We’ll say that you took a step down every time you were drained by a point, and a step up every time you charged by a point. We’ll say that when you hit 100% you always unplug (you can’t take a step up over 100).

A question is: how many ways are there to take 100 steps from 100%; how many paths are there in all the different combinations of up and down steps? And for any given charge level, how many ways are there to that point from 100% that involve exactly 100 steps? 0% only has one path leading to it: there is only one way to take 100 steps down from 100%. The 2% level has about 100 paths leading to it: a hundred ways to take 98 steps down with a little goosestep up and down at some point between the top and bottom. There are a lot of paths from 100% back to 100%: you can go down 50 and up 50, you can go down and up 50 times, you can go down and up by 4 then 7 then 15.

With these ideas, we’re now to our key question. Which charge level between 0 and 100 has the greatest number of paths leading to it? The 68% charge level is the one with the greatest number of paths leading to it (0% has the fewest). Another way of saying the same thing: if you randomly generate paths of length 100, up and down, over and over, the number you’ll land on the most is 68%. Not by a lot, but if I know nearly nothing about your phone—it’s got about a day of charge, it’s near the end of the day, you’re on the move enough that it’s often but not usually plugged in—the least bad guess is that you’re at about 60-70% charge by the end of the day.

The orthography of number

In the next book you pick up, keep an eye out for the first number you see, not spelled out but in digits. Will it be big, or little? Even or odd? What can we say about the numbers that are dealt to us, numbers about anything: dollars, marbles, people, fish? The fun thing about pure reason is a) you will learn something interesting, and b) you won’t get to choose what. According to Benford’s Law, the next number you see, big or small, is most likely to start with a 1. A number starting with 1 is 30%! That ends up being about 12% more likely than 2, which is about 5% more likely than 3, and so on down to 9, which initiates only 4.6% of numbers, not 11% like you’d expect (11=100/9 digits; you don’t divide by 10 because in Arabic numerals the only number than can start with the tenth digit, 0, is 0). I don’t understand it perfectly but it’s got something to do with there being more small numbers than big numbers, with logarithms, and with Arabic numerals. They come together to give 1’s center-stage. I don’t know if this is a metaphor or the actual explanation, but if you look at the way a slide rule gives physical space to each digit according to the logarithmic way of representing “bigness”, you’ll see that 1 gets more space than any of the others, and in that way gets more real estate in our lives, with pride of place on the far left of most written numbers.

It might sound far fetched to say, but pure reason, charged with statistical theory, and seeded with one observation, can help you shower comfortably, find your keys quickly, and keep your phone alive. It can probably also help you brush your teeth, clean your windows, and wash the dishes; let me know what you find.

I’m often surprised at how casual so many communities are about who they let in. To add people to your membership is to steer your community in a new direction, and you should know what direction that is. There’s nothing more powerful than a group of aligned people, and nothing more difficult than steering a group when everyone wants something different for it. I’ve seen bad decisions on who to include ruin many communities. And, on the other hand, being intentional about it can have a transformative effect, leading to inspiring alignment and collaboration. The best collaborations of my life have all been in discerning communities.

So what does it mean to be intentional about membershipping? You could say that there are two overall strategies. One is to go slow and really get to know every prospective member before inviting them fully into the fold. The other is to be very explicit and providing narrow objective criteria for membership. These both have upsides and downsides. If you spend a lot of time getting to know someone, there will be no surprises. But this can produce cliqueishness and cronyism: who else have you spent that much time with than your own friends? On the other hand are communities that base membership on explicit objective criteria can be exploited. A community I knew wanted tidy and thoughtful people, so would filter people on whether they helped with the dishes and brought desert. The thinking was that a person who does those things naturally is certainly tidy and thoughtful. But every visitor knew to bring desert and help with the dishes, regardless of what kind of person they were, so the test failed as an indicator.

We need better membershipping processes. Something with the fairness and objectivity of explicit criteria, but without their vulnerability to being faked. There are lots of ways that scholars solve this kind of problem. They will theorize special mechanisms and processes. But wouldn’t it be nice if we could select people who just naturally bring desert, help with dishes, ask about others, and so on? Is that really so hard? To solve it, we’re going to do something different.

The mechanism: the double-blind policy process with collective amnesia

Amnesia is usually understood as memory loss. But that’s actually just one kind, called retrograde amnesia, the inability to access memories from before an event. The opposite kind of amnesia is anterograde. It’s an inability to form new memories after some event. It’s not that you lost them, you never got them in the first place. We’re going to imagine a drug that induces temporary anterograde amnesia. It prevents a person from forming memories for a few hours.

To solve the problem of bad membershipping, we’re going to artificially induce it in everyone. Here’s the process:

1. A community’s trusted core group members sit and voluntarily induce anterograde amnesia in themselves (with at least two observers monitoring for safety).
2. In a state of temporary collective amnesia, the group writes up a list of membership criteria that are precise, objective, measurable, and fair. As much as possible, items should be the result of deliberation rather than straight from the mind of any one person.
3. They then seal the secret criteria in an envelope and forget everything.
4. Later, the core group invites a prospective new member to interview.
5. The interview isn’t particularly well structured because no one knows what it’s looking for. So instead it’s a casual wide-ranging affair involving a range of activities that really have nothing to do with the community’s values. These activities are diverse and wide-ranging enough to reveal a variety of dimensions of the prospectives personality. An open-ended personality test or two could work as well. What you need is a broad activity pool that elicits a range of illuminating choices and behaviors. These are being observed by the membership committee members, but not discussed or acted upon until ….
6. After the interview, a group of members sits to deliberate on the prospective’s membership, by
   • collectively inducing anterograde amnesia,
   • opening the envelope,
   • recalling the prospective’s words and choices and behavior over the whole activity pool,
   • judging all that against the temporarily revealed criteria,
   • resealing the criteria in the envelope,
   • writing down their decision, and then
   • forgetting everything
7. Later this membership committee reads the decision they came to to find out if they will be welcoming a new peer to the group.

The effect is that the candidate got admitted in a fair, systematic way that can’t be abused. Why does it work? No one knows how to abuse it. In a word, you can’t game a system if literally nobody knows what its rules are. Not knowing the rules that govern your society is normally a problem, but it seems to be just fine for membership rules, maybe because they are defined around discrete intermittent events.

Psychoactives in decision-making

If this sounds fanciful, it’s not: the sedatives propofol and midazolam both have this effect. They are common enough in the cocktails of sedatives, anesthetics, analgesics, and tranquilizers that anaesthesiologists administer during surgical procedures.

If this sounds feckless or reckless, it’s not. There is an actual heritage of research that uses psychoactives to understand decision-making. I’m a cognitive scientist who studies governance. I learned about midazolam from Prof Richard Shiffrin, a leading mathematical psychologist and expert in memory and decision-making. He invoked it while proposing a new kind of solution to a social dilemma game from economic game theory. In the social dilemma, two people can cooperate but each is tempted to defect. Shiffrin suggests that you’ll cooperate if the person is so similar to you that you know they’ll do whatever you do. He makes the point by introducing midazolam to make it so the other person is you. In Rich’s words:

You are engaged in the simple centipede game decision tree [Ed. if you know the Prisoner’s Dilemma, just imagine that] without communication. However the other agent is not some other rational agent, but is yourself. How? You make the decision under the drug midazolam which leaves your reasoning intact but prevents your memory for what you thought about or decided. Thus you decide what to do knowing the other is you making the other agent’s decision (you are not told and don’t know and care whether the other decision was made earlier or after because you don’t remember). Let us say that you are now playing the role of agent A, making the first choice. Your goal is to maximize your return as agent A, not yourself as agent B. When playing the role of agent B you are similarly trying to maximize your return.

The point is correlation of reasoning: Your decision both times is correlated, because you are you and presumably think similarly both times. If you believe it is right to defect, would you nonetheless give yourself the choice, knowing you would defect? Or knowing you would defect would you not choose (0,0)? On the other hand if you think it is correct to cooperate, would it not make sense to offer yourself the choice? When playing the role of B let us say you are given the choice – you gave yourself the choice believing you would cooperate – would you do so?

— a 2021/09/15 email

The upshot is that if you know nothing except that you are playing against yourself, you are more likely to cooperate because you know your opponent will do whatever you do, because they’re you. As he proposed it, it was a novel and creative solution to the problem of cooperation among self-interested people. And it’s useful outside of the narrow scenario it isolates. The idea of group identity is precisely that the boundaries of our conceptions of ourselves can expand to include others, so what looks like a funny idea about drugs is used by Shiffrin to offer a formal mechanism by which group identity improves cooperation.

Research at the intersection of drugs and decision-making isn’t restricted to thought experiments. For over a decade, behavioral economists in the neuroeconomics tradition have been piecing together the neurophysiology of decision-making by injecting subjects with a variety of endogenous and exogenous substances. For example, see this review of the effects of oxytocin, testosterone, arginine vasopressin, dopamine, serotonin, and stress hormones.

Compared this other work, all that’s unusual about this post is the idea of administering to a whole group instead of individuals.

Why save democracy when you can save dictatorship? | The connection to incentive alignment

This mechanism is serious for another reason too. The problem of membershipping is a special case of a much more general problem: “incentive alignment” (also known as “incentive compatibility”).

• When people answering a survey tell you what they want you hear instead of the truth
• When someone lies at an interview
• Just about any time that people aren’t incentivized to be transparent

Those are all examples of mis-alignment in the sense that individual incentives don’t point to system goals.

Incentive compatibility is especially challenging for survey design. That’s important because surveys are the least bad way to learn things about people in a standardized way. Incentive compatible survey design is a real can of worms.

That’s what’s special about double-blind policy. It’s a step in the direction of incentive compatibility for self-evaluation. You can’t lie about a question if nobody knows what was asked.

Quibbles

For all kinds of reasons this is not a full solution to the problem. One obvious problem: even if no one knows the rules, anyone can guess. The whole point of introducing midazolam into the social dilemma game was that you know that you will come to the same conclusions as yourself in the future. So just because you don’t know the criteria doesn’t mean you don’t “know” the criteria. You just guess what you would have suggested, and that’s probably it. To solve this, the double-blind policy mechanism has to be collaborative. It requires that several people participate, and that a collaborative deliberation process over many members will produce integrated or synergistic criteria that no single member would have thought of.

Other roles for psychoactives in governance design

The uses of psychoactives in community governance are, as far as I know, entirely unconsidered. Some cultures have developed ritualistic sharing of tobacco or alcohol to formalize an agreement. Others have developed ordering the disloyal to drink hemlock juice, a deadly choline antagonist. That’s all I can think of. I’m simultaneously intrigued to imagine what else is out there and baseline suspicious of anyone who tries.

The ethics

For me this is all one big thought experiment. But I live in the Bay Area, which is governed by strange laws like “The Pinocchio Law of The Bay” which states:

“All thought experiments want to go to the San Francisco Bay Area to become real.”

(I just made this up but it scans)

Hypothetically, I’m very pleased with the idea of solving governance problems psychoactives, but I’ll admit that it suffers from being awful-adjacent: It’s very very close to being awful. I see three things that could tip it over:
1) If you’re not careful it can sound pretty bad, especially to any audience that wants to hate it.
2) If you don’t know that the idea has a legitimate intellectual grounding in behavioral science, then it just sounds druggy and nuts.
3) If it’s presented without any mention of the potential for abuse then it’s naive and dangerous.

So let’s talk about the potential for abuse. The double-blind policy process with collective amnesia has serious potential for abuse. Non-consensual administration of memory drugs is inherently horrific. Consensual administration of memory drugs automatically spawns possibilities for non-consensual use. Even if it didn’t, consensual use itself is fraught, because what does that even mean? The framework of consent requires being able and informed. How able and informed are you when you can’t form new memories?

So any adoption or experimentation around this kind of mechanism should provide for secure storage and should come with a security protocol for every stage. Recording video or having observers who can see (but not hear?!) all deliberations could help. I haven’t thought more deeply than this, but the overall ethical strategy would go like this: You keep abuse potential from being the headline of this story by credibly internalizing the threat at all times, and by never being satisfied that you’ve internalized it enough. Expect something to go wrong and have a mechanism in place for nurturing it to the surface. Honestly there are very few communities that I’d trust to do this well. If you’re unsure you can do it well, you probably shouldn’t try. And if you’re certain you can do it well, then definitely don’t try.

There’s this old organizer wisdom that freedom is an endless meeting. How awful. Here the sprightly technologist steps in to ask:

“Does it have to be? Can we automate all that structure building and make it maintain itself? All the decision making, agenda building, resource allocating, note taking, emailing, and even trust?
We can; we must”

That’s the popular hypothesis, that technology should fix democracy by reducing friction and making it more efficient. You can find it under the hood of most web technologies with social ideals, whether young or old. The people in this camp don’t dispute the need for structure and process, but they’re quick to call it bureaucracy when it doesn’t move at the pace of life, and they’re quick to start programming when they notice it sucking up their own free time. Ideal governance is “the machine that runs itself“, making only light and intermittent demands for citizen input.

And against it is the unpopular hypothesis. What if part of the effectiveness of a governance system is in the tedious work of keeping it going? What if that work builds familiarity, belonging, bonding, sense of agency, and organizing skills? Then the work of keeping the system up is itself the training in human systems that every member needs to have for a community to become healthy. It instills in every member pragmatic views of collective action and how to get things done in a group. Elinor Ostrom and Ganesh Shivakoti give a case of this among Nepali farmers when state-funds replaced hard-to-maintain dirt irrigation canals with robust concrete irrigation canals and farmer communities stopped sharing water equitably. What looked like maintaining ditches was actually maintaining an obligation to each other.

That’s important because under the unpopular hypothesis, the effectiveness of a governance system depends less on its structure and process (which can be virtually anything and still be effective) and more on what’s in the head of each participant. If they’re trained, aligned, motivated, and experienced, any system can work. This is a part of Ostrom’s “institutional diversity”. The effective institution focuses on the members rather than the processes by making demands of everyone, or “creating experiences.”

Why are organizations bad computers? Because that isn’t their only goal.

In tech circles I see a lot of computing metaphors for organizations and institutions. Looking closer at that helps pinpoint the crux of the difference between the popular and unpopular hypotheses. In a computer or a program, many gates or function are linked into a flow that processes inputs into outputs. In this framework, a good institution is like a good program, efficiently and reliably computing outputs. Under the metaphor all real-world organizations look bad. In a real program, a function will compute reliably, quickly, and accurately without having to provide permission or buy-in or interest? In an organization each function needs all those things.

So organizations are awful computers. But that’s not a problem because it’s goal isn’t to compute, but to compute things that all the functions want computed. It’s a computer that exists by and for its parts. The tedium of getting buy-in from all the functions isn’t an impediment to proper functioning, it is proper functioning. The properly functioning organization-computer is constantly doing the costly hygiene of ensuring the alignment of all its parts, and if it starts computing an output wrong, it’s not a problem with the computer, it’s a problem with the output.

If the unpopular hypothesis is right, then we shouldn’t focus on processes and structures—those might not matter at all—but on training people, keeping them aligned with each other, and keeping the organization aligned with them. It supports another hypothesis I’ve been exploring, that all governance is onboarding.

Less Product, more HR?

This way of thinking opens a completely different way of thinking about governance. Through this lens,

• Part of the work of governance is agreeing what to internalize
• a rule is the name of the thing that everyone agrees that everyone should internalize.
• The other part of governing is creating a process that helps members internalize (whether via training, conversation, negotiation, even a live-action tabletop role playing simulation).
• once it’s internalized by everyone the rule is irrelevant and can be replaced by the next rule to work on.

In this system, the constraints on the governance system depend on human limits. You need rules because an org needs to be intentional about what everyone internalizes. You’ll keep needing rules because the world is changing and the people are changing and so what to internalize is going to change. You can’t have too many rules at one time because people can’t remember too rules-in-progress at once. You need everyone doing and deciding the work together because it’s important that the system’s failures feel like failures of us rather than them.

With all this, it could be tempting to call the popular hypothesis the tech friendly one. But there’s still a role for technology in governance systems following the unpopular hypothesis. It’s just a change in focus, into technologies that support habit building, skill learning, training, onboarding, and that monitor the health of the shared agreements underlying all of these things. It encourages engineers and designers to move from the easy problems of system and structure to the hard ones of culture, values, and internalization. The role of technology in supporting self-governance can still be to make it more efficient, but with a tweak: not more efficient at arranging parts into computations, but more efficient at maintaining its value to those parts.

Maybe freedom is an endless meeting and technology can make that palatable and sustainable. Or maybe the work of saving democracy isn’t in the R&D department, but HR.