Hi there, argmin readers! Today’s post is a live blog of Class 18 of my graduate seminar “Forecasting: A Critical Retrospective.” In this class, we covered one of my favorite topics: Defensive Forecasting. The syllabus and list of past posts are here.

We’ve spent the semester examining application areas with strong cultures of forecasting. But one of the central reasons I proposed this class in the first place was to examine the culture of forecasting itself. American society is obsessed with applying forecasting, prediction markets, and gambling to… everything. We’ll spend the remaining classes investigating this oppressive culture.

Next class we’ll discuss prediction markets, and in the following we’ll get to that whole p(doom) thing. But to talk about both, we first have to step back and return to a logical fallacy of forecasting raised in the first lecture of the class and by Saint Augustine millennia ago.

Certainly, we believe that if you have a good understanding of a system, you should be able to predict its future trajectory on some reasonable time horizon. We can quibble about how long such a projection would be, but understanding implies some ability to talk through potential future outcomes and their likelihoods. But what about the converse? If you can predict the future, does that mean you understand the world? The answer is no, and you can mathematically prove it.

Superforecasters themselves say you can train yourself to be better at forecasting. This training requires no expert domain knowledge. They advise you to find the best set of past events that match the thing you are trying to predict (i.e., find the reference class). You are then told to compute the base rate in that reference class. Then, you are supposed to nudge the base rate based on whether new information makes the event more or less likely than in the past. This last step is the least well-specified, but you guide yourself by making sure that your track record remains well-calibrated. Following these rules, good forecasting is and should be mostly algorithmic bookkeeping devoid of domain knowledge. You could certainly write computer code to do it. You don’t even need an LLM. A good forecaster is a mechanical pattern recognizer.

Mechanical pattern recognition is great because it doesn’t require understanding. This is why machine learning is such a powerful technology.

You can make this very formal using the framework of Defensive Forecasting, a term coined by Vladimir Vovk, Akimichi Takemura, and Glenn Shafer to describe a class of algorithms that mechanize the meta-forecasting approach I describe above. This work has connections to paradoxes in calibration raised by Foster and Vohra in the 90s, who showed you could produce well-calibrated predictions knowing nothing about data-generating processes. It is closely related to Blackwell Approachability, where we aim to adaptively steer multiple objectives at once. Blackwell approachability is also equivalent to no-regret learning, so our friend online gradient descent can be interpreted as clever bookkeeping. Defensive forecasting is also equivalent to recently developed frameworks for multicalibration, and hence subsumes the problem of outcome indistinguishability.

Juanky Perdomo and I wrote what we hope is an accessible introduction to this topic, laying out all of these connections in as elementary a way as we could. One simple idea makes the whole thing work.

That idea is perhaps easiest to describe in the language of outcome indistinguishability. We know from the law of large numbers that the variance of a bunch of iid draws from a Bernoulli distribution shrinks at a rate of one divided by the number of draws. If a set of outcomes tracks a set of predictions at this rate, then it’s impossible to say the outcomes weren’t sampled from a probability distribution defined by those probabilistic predictions. Defensive forecasting exploits this indistinguishability. It turns out you can always pick a prediction so that it looks like the law of large numbers held. Moreover, you can find this prediction by correcting errors that pulled you away from the law of large numbers in the past.

This is possible because the evaluation rules are proposed in advance. These rules can always be reduced to some sort of moment-matching problem (i.e., a multicalibration problem), and moment matching with defensive forecasting can be derived using elementary algebra. For a simple example of this reduction, check out this blog post from last year. For the full details of the reduction, see Section 5 of my paper with Juanky linked above.

The metrics we use to study prediction fidelity of uncertain events are all gameable in the sense that they can be maximized without a “world model.”1 These metrics include calibration checks and proper scoring rules. Forecasting is not about understanding. It’s about meeting expectations in an evaluation game. Once the rules are set, the method is determined. Gather as many covariates as you can, write down the appropriate moments to match, and then just let the machine sort it out.

There is no better illustration of metrical determinism than forecasting. The question and evaluation wholly determine the forecast. And that’s where we should focus our inquiry: why are we forecasting these things? And how are we judging forecasts? Once we decide what we’re forecasting, the best forecasting strategy is predetermined. We can’t know the future, but we can mechanically generate forecasts that look like the future came from our model. This seductive trap makes us think forecasters know something we don’t. Heed Saint Augustine’s advice and don’t fall for it.

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Hi there, argmin readers! Today’s post is a late and brief reaction to a tiny subplot of yesterday’s historic election: the widespread rejection of AI datacenters. It was inspired by an insightful Dan Davies thread on bluesky that I have been unable to get out of my head.

Elections are a muddled measurement of “public opinion,” but they’re probably the only real measurement we get. And with every surprising measurement, a good rational agent must reflect on its beliefs. So what should we passive rational observers make of this historically large swing towards the Democratic Party in yesterday’s vote?

Obviously, this is a major repudiation of Donald Trump, his policies, and the Republican Party. However, you readers probably don’t come here for my political takes, and I don’t want to use this Substack for them anyway. Even if it wasn’t the biggest issue on the ballot, something closer to home is worth pondering. The American people are loud and clear that they hate AI.

Nearly fifty measures explicitly about building data centers appeared on ballots across the nation. All of them look like they will vote to limit further construction. A datacenter moratorium was part of Gina Hinojosa’s platform in her successful bid to become the first Democratic Party governor of Texas in over 30 years. The anti-datacenter position was undeniably the winning one. Poll results from this last summer showed people would rather have a coal plant in their backyard than a datacenter. Now elections confirm these sentiments were real.

We could try to convince ourselves that this sentiment is just about datacenters themselves. They are gross, gigantic buildings that employ no one, make a ton of noise, and are often powered with dirty energy. Who would want one of those? But datacenters are also a big, ugly, legible signal of a deeply unpopular industry.

At some point, we techy folks have to reckon with how much people hate what we build. We can point to revealed preferences all we want (people are adopting it! It’s making money!), but we did this during the social media boom of the 2010s (people spend a ton of time doomscrolling, therefore it’s good!). These economic numbers are also measurements, but we have to reconcile them with other data. Adoption and economic growth are so concentrated in so few hands that, while this props up our stock indices, it doesn’t lead to tangible benefits for everyone else.

Certainly, it doesn’t help that the industry has been selling itself as coming for everyone’s jobs. It doesn’t help that many prominent people working at these companies take to social media to gleefully exclaim that they think there’s more than a 10 percent chance that their company will kill everyone on earth. It doesn’t help that the big AI companies have been caught committing felonious cybercrimes all summer. It also doesn’t help that the leaders of these companies have been quite visibly embracing the Trump administration. Hugging a loser is a bad look, guys.

It’s a shame, because the technology is truly amazing. The AI true believers (accidentally) built something very cool that I would not have thought possible five years ago. But this amazing technology makes everyone miserable! It even immiserates its biggest boosters, who get sucked into productivity doom loops managing swarms of agents that speak in a unison chorus of Claudish. What’s our positive case here? The torment nexus of “superintelligence” ain’t it.

I have a lot of friends, colleagues, and alums who make a living building AI models. And I guess a bunch will be infinitely rich after the upcoming IPOs. But if you’re working for something more hated than the tobacco industry, maybe it’s way past time you stood up to your employer and demanded a better direction. And no, an open letter doesn’t count.

I’m not hopeful that this will happen. Ten years ago, I wrote a blog post shell-shocked by the election of Trump and disgusted with my industry. The cameo from Sam Altman explains a lot of my pessimism. I’ve been soul-searching for a decade. The leaders of the tech industry, instead of offering a positive vision and doing better, ended up sucking up to the new authoritarian government. They did it with pouting and feet dragging in 2016. They did it with their chests out in a celebratory embrace in 2024.

Our industry and field need a complete reboot. But that requires collective action. How do we fix it? What do we do next? I’d love to hear your thoughts on how the tech sector can clean up its image and make a positive, populist case for itself.

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Hi there, argmin readers! Today’s post is a live blog of Class 17 of my graduate seminar “Forecasting: A Critical Retrospective.” In this class, we’re going to discuss simulation as a means of prediction. The syllabus and list of past posts are here.

In a surprisingly dark survey paper from 1971, “Counterintuitive Behavior of Social Systems,” electrical engineer turned social scientist Jay Forrester made a case for informing public policy with computer simulations. Forrester argued that policymakers made all decisions with models, but his computer models were more explicit and concrete than people’s mental models. Computer models laid all of the assumptions on the table and let stakeholders adjust the parameters until they conformed to reality. They also let people create a variety of prefactual worlds, demonstrating plausibility and illustrating the consequences of various decision-making paths. Most importantly for Forrester, the computer models captured the surprising and unintuitive nature of feedback effects, showing pathways that mental models might not have predicted.

Forrester’s survey gives three examples, each with more ambitious aims than the last. He describes his time as a management consultant and how computer simulations revealed that decisions meant to fix things led to worse outcomes. Good intentions could lead to a “downward spiral,” and this would often convince managers to double down on their initial wrong decision. Forrester argues that a simulation would have predicted these troubles and informed management of a better path.

He then turns these ideas toward urban planning. He claims that his simulations can explain and fix the “depressed nature of central cities.” Indeed, his simulations argue that four well-intentioned liberal programs are causing urban blight, not fixing it.

“One program was creation of jobs by busing the unemployed to suburban jobs or through governmental jobs as employer of last resort. Second was a training program to increase skills of the lowest-income group. Third was financial aid to depressed cities from federal subsidies. Fourth was construction of low-cost housing.”

Forrester goes on to explain the vicious cycle here, where a surplus of cheap housing draws in more new residents than the job market can support. This leads to overcrowding and a less attractive urban environment. This, in turn, repels new affluent residents. Forrester says his simulations “both confirm and explain much of what has been happening over the last several decades in cities.”

A dispassionate observer might say that his simulation matched his politics. But Forrester saw modeling power, not confirmation bias. He went on to extend his models to a global scale.

Forrester goes on to describe work he had done that predicted the end of the world by 2071. Current trends could not support population growth, and pollution would run amok, and we’d run out of natural resources. The only solution was to impose policies that swiftly dampened population growth and austerely conserved resources. Applying Forrester’s simulator, a team led by Dennis Meadows assembled the dire predictions into the 1972 book The Limits to Growth, which sold 12 million copies worldwide.

Forrester’s report is filled with feedback diagrams and simulation traces. The ability to predict so many different possibilities under different scenarios is intoxicating. Historian Kevin Baker argues that this sort of interactive experience was core to the allure of the simulation model. By adding knobs and switches, people could play out different worlds, making the simulation feel more trustworthy and real. This would eventually lead to enthralling games with bizarre hidden politics, notably the world bestseller SimCity. As Baker puts it, “The capacity of simulation models to captivate and enthrall is taken for granted as a natural property of simulation. But these abilities were often deliberately engineered into software for historically-specific purposes.” Forrester loved his simulators because they quantified and externalized mental models. He underemphasized how they created new mental models, letting policymakers play video games in imaginary worlds that let them feel as if they were creating the future.

One of the funnier things about statistical prediction is that it forecasts a static world. Your best guess is to mimic past rates. By contrast, simulation can imagine different worlds, mechanistically mapping trajectories into the future based on our assumptions about the present.

However, simulations are not reality, and more sophistication is not good in and of itself. In fact, if small changes lead to unexpected consequences, a single poor modeling choice can too. The doom of The Limits to Growth did not play out. Nor did Forrester’s libertarian predictions about urban blight.

In the last class session, we grappled with two competing sales pitches for “silicon sampling.” Most people felt comfortable using silicon samples as part of some prediction loop. For example, you could create virtual training data for some recommendation system by asking LLMs to simulate answers to questions based on demographics. You might have it label examples while “pretending to be a plumber” and then “pretending to be a schoolteacher,” using those labels as synthetic training data. You can then validate the resulting system against standard KPIs with A/B tests or benchmarks. If the prediction system passes evaluation metrics, it doesn’t matter if it accurately models people.

On the other hand, it’s easy to believe that because LLMs perform well on these prediction tasks, they create realistic simulations of people. You can interactively inspect the answers LLMs give and gain trust in their fidelity. And then you can convince yourself that you can use these simulations to understand human behavior without talking to people. This is the same seductive simulation loop that Baker calls out. We’re more skeptical of simulation now than in 1970, likely because we’re so familiar with video games and how they aren’t real. But the prospect of simulating society is still enticing, and new well-funded research programs and startups are playing the same old tricks of immersive gameplay.

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Hi there, argmin readers. Today I’m Monday Morning Quarterbacking and wrote one of my sporadic football analytics posts.

NFL Sunday was a wild and weird one. Rare events dominate the NFL and are what makes it so fun to watch. The Tampa Bay Bucs destroyed the Atlanta Falcons in a hurricane, rushing for 324 yards and passing for… zero yards. Zero! They didn’t even complete a pass. No team had won a game with zero completions in over fifty years. The Broncos, quarterbacked by Bo Nix, orchestrated his twelfth comeback win down double digits in the fourth quarter. He’s only started 42 games! And yet, everyone, including his coach, still thinks Bo Nix is a bad quarterback. And yesterday was a banner day for my favorite hobby horse, the stupidity of the go-for-2-down-8 (G42D8) gambit.

To the relief of most of my readership, I haven’t written about G42D8 in a while. So let me remind those who are fortunate enough not to share my dumb obsession. A team down 14 points in the fourth quarter starts a comeback by scoring a touchdown. They are now down by 8. They face the decision to kick an extra point or attempt a 2-point conversion. In 2015, analytic-brained weirdos convinced themselves that the laws of probability insisted your chances of winning were only 50% if you kicked the extra point, but were 62.5% if you attempted the 2-point conversion, even if you missed the first one. And for the next decade, they’d show you this stupid infographic and smugly yell about the probability differential to show you how smart they are.

Late in the third quarter, down 17-3 to the Cowboys, the Cardinals benched journeyman quarterback Jacoby Brissett for journeyman backup quarterback Gardner Minshew. The Cardinals immediately scored on a 63-yard run by Tyler Allgeier. Allgeier was apparently stoked about the QB change. Down 8, they kicked the extra point. Even though it was technically still 57 seconds until the fourth quarter, G42D8 zealot Seth Walder exclaimed they should have gone for two. Regardless, the Cardinals faced the down-eight test again after finding themselves again down 14 a few minutes into the fourth quarter. They scored a touchdown and kicked the extra point. The Cardinals failed the G42D8 test, twice in a single game. They weren’t having any of this shamalytics. Of course, they went on to win.

In 2024, I wrote about the full logic of the G42D8 gambit and why it was a terrible misapplication of decision theory.1 Since the start of the 2025 season, teams attempted the 2-point when down 8 13 times. Teams kicked extra points 11 times. The strategy is certainly mainstream enough now that teams apply it more than half the time. And announcers remain completely befuddled every time. The announcers are not wrong. The analytic explanation is not “simple math.” It’s tortured, mathematicized reasoning.

But since it’s becoming the dominant strategy for losing teams, it’s worth checking how those teams fare. The G42D8 gambit teams won 2 of the 13 games where they followed the analytics (and one win is a clear technicality, which I’ll address in a second). The stodgy, conservative, meathead teams won… twice as well. In fact, they additionally tied once. That is, team G42D8 is 2 and 11 (.154 pct). Team Meathead is 2, 8, and 1 (.227 pct).

Yes, these sample sizes are absurdly small, and it’s impossible to say one is better than the other. That is actually my point. We decide NFL seasons with 17 games, after all. There is no evidence that G42D8 leads to more wins than kicking extra points.

Since 2015, 45 teams have attempted the G42D8 gambit. In these games, 22 teams have missed the first two-point conversion. The G42D8 brain geniuses tell us this is okay, because when they score the second touchdown, they can go for two again and take the game to overtime. Except that in all 22 of these games, no team has ever taken the game to overtime. 19 of these teams never scored another touchdown! In one game, the Browns scored the second touchdown but missed the second 2-point conversion and lost. In another, the Jets made the 2nd 2-point conversion, but there was still 4:30 left in the game, and the Lions subsequently marched down the field to score a winning touchdown. The truly bizarre remaining game was a Thursday Night Football NFC South masterpiece between the aforementioned enemies, the Falcons and Bucs (IYKYK). The Falcons missed the 2nd 2-point conversion, but took advantage of miserable clock management by Bucs coach Todd Bowles and managed to get a third possession. They kicked a field goal to win by 1.2

A third possession in regulation isn’t even considered a possibility in the G42D8 decision tree, where you lose 100 percent of the time you miss both conversions. Except the Falcons miraculously won. I’ll allow this one to stay in the win column for team G42D8, but it’s certainly a technicality, and certainly one that shows football strategies are far more complex than what can be captured in an infographic. The models don’t describe the game of football as much as the statistical analysts think they do.

If you’re going to insist you’re smarter than everyone, at some point you need to show results. Otherwise, the people who don’t even understand what “percent” means are going to stuff you in a locker. Down 14 points in the fourth quarter means you’re probably going to lose. You can go for two. You can go for one. But trying to argue that one is obviously superior to the other is, and always will be, dumb. Just like fighting with people on sports shows and social media.

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Hi there, argmin readers! Today’s post is about the history of failing to rigorously define efficiency in computer science. Like my previous post on Fourier transforms, it’s more technical than usual, but I tried to make it as accessible as possible.

I’ve always been fascinated by this pernicious pattern in the practice of applied mathematics, which I wrote about here a few weeks ago:

Applied mathematicians often need to build a giant scaffolding of mathematical modeling to solve a problem. This scaffolding creates new mathematical puzzles that aren’t directly connected to the original problem of interest, but that entice problem solvers. You’ll then see dozens of follow-up papers solving the puzzles but forgetting the problem we cared about in the first place.

There is probably no better example of such forgetting than the field of complexity theory.

In 1965, Jack Edmonds came up with a clever way to find a maximum matching in a graph. He wanted to argue that his algorithm could be computed “efficiently,” as the procedure was a bit complicated and required a computer to run. But he found he didn’t have the language to describe what it would mean for an algorithm to be efficient. In Section 2 of his paper, named “Digression,” he wrote,

According to the dictionary, “efficient” means “adequate in operation or performance.” This is roughly the meaning I want—in the sense that it is conceivable for maximum matching to have no efficient algorithm. Perhaps a better word is “good.”

I am claiming, as a mathematical result, the existence of a good algorithm.

Edmonds noted that he could enumerate every possible solution to the matching problem and find the largest one. This would be a correct algorithm. However, the number of total matchings is exponentially large in the size of the graph. Blindly writing all possible matchings down and picking the one that achieved the maximum was a “not good” algorithm. You might call it a “bad” algorithm. His new procedure was vastly more efficient.

So Edmonds spent two pages constructing a definition of good. He demanded that everyone agree on a reasonable definition for a problem size. For his matching problem, he said the size was the number of vertices plus the number of edges in the graph. A good algorithm would then have a running time upper-bounded by some well-defined function of that size, no matter how large the instance. He demanded that the running-time bound hold for every conceivable size, because he feared someone might rig the problem by planting a few small instances that were unnaturally hard.

Edmonds wasn’t completely satisfied with this definition. Indeed, he wrote:

It would be unfortunate for any rigid criterion to inhibit the practical development of algorithms which are either not known or known not to conform nicely to the criterion. Many of the best algorithmic ideas known today would suffer by such theoretical pedantry. In fact, an outstanding open question is, essentially: “how good” is a particular algorithm for linear programming, the simplex method? And, on the other hand, many important algorithmic ideas in electrical switching theory are obviously not “good” in our sense.1

With this caveat noted, he concluded his digression by announcing the complexity of his new blossom algorithm: “An upper bound on the order of difficulty of the matching algorithm is n⁴, where n is the number of vertices in the graph.”

Edmonds did not make any further arguments for what he meant by good. He asserted that exponential time is bad. For most algorithm designers, linear time, proportional to the input length, was naturally excellent. Moreover, our grade-school multiplication algorithm took quadratic time (multiply two three-digit numbers out by hand like you were taught in school and count the number of digits you write down when you calculate it), and that seemed pretty good. Edmonds had a matching algorithm that required a quartic number of operations. To later formalists like Richard Karp, it seemed like a “polynomial” number of operations was a reasonable definition for goodness. Polynomial time is good. Exponential time is bad. This created the field of complexity theory, with the goal of proving that all sorts of algorithms run in polynomial time and characterizing the problems for which no polynomial-time algorithm existed.

But polynomial time probably haunted Edmonds. It is not a “good” algorithm if your procedure scales like n¹⁰⁰⁰, even if this is technically a polynomial. More absurdly,

is a polynomial bigger than the exponential function 2ⁿ for any n we could ever encounter. Polynomial was always an imperfect definition of good, but we ran with it. Thousands of papers later, we just have a zoo of confusing complexity results unmoored from the realities of computation.

Indeed, asymptotic thinking about how polynomials differ from exponentials enables the bad habit of designing “galactic algorithms,” conceptual procedures with running times so large they could never be implemented in our universe. I mentioned these in my earlier post about OpenAI’s Faster Fourier Transform.

This brings me back to our beneficent friends at OpenAI. This week they declared their latest breakthrough in theoretical computer science. They provided an algorithm for the satisfiability problem that ran in “subexponential time.” Satisfiability is one of the most well-known “NP complete problems, and I don’t want to go into the details of P vs NP today, but suffice it to say that you would win a Clay Millennium Prize if you could find a polynomial-time algorithm for satisfiability.2

Now, subexponential time does not mean polynomial time. It merely means that the running time can be bounded as

Where n is the problem size, and f is a “sublinear” function, meaning the limit of f(n)/n goes to zero as n goes to infinity.

Indeed, in the case of OpenAI’s new algorithm for the satisfiability problem, the bound was

For some unspecified constant numbers d and C. Ugly as this expression is, this was touted on Twitter as the biggest moment in theoretical computer science in 50 years. It was covered all over the tech press this week. OpenAI clearly wanted us to think it was a big fucking deal. And many theoretical computer scientists took to social media to agree.

Since it was such a big deal, I wanted to see if I could understand the algorithm a bit. Of course, as I’ve told all of you, we’re not supposed to read these papers. We’re supposed to ask ChatGPT what they say. And ChatGPT told me there was a catch.

The derived algorithm runs exhaustive search—the algorithm Edmonds declared bad in 1965—if the number of variables is less than 10^10,000,000,000,000,000,000,000,000.

This is a completely unfathomable number.3 There are something like 10^80 atoms in the universe. That’s 10^9,999,999,999,999,999,999,999,920 times smaller. Up until this barely finite threshold, the magic new algorithm calls an exponential-time subroutine. For any problem that we could ever consider, the procedure is exponential time. The “result” is that only in some bizarre, unknowable neighborhood of infinity, satisfiability problems are solved in subexponential time.

The claimed subexponential algorithm for satisfiability is definitive evidence that our definition of efficient was even worse than we thought it was 50 years ago. The answer tells us nothing about efficiency or goodness. Sometimes you need to answer your question to realize you wanted something else.

I’m not a betting man, but I have a prediction. It’s going to turn out that P=NP in some galactic sense, and all we’ll learn is that we spent fifty years answering the wrong question.

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Hi there, argmin readers! Today’s post is a live blog of Class 16 of my graduate seminar “Forecasting: A Critical Retrospective.” In this class we’re going to dig into the bizarre world of silicon sampling. I remain befuddled! The syllabus and list of past posts are here.

In 2024, at a secluded conference in the high desert, Kevin Munger told me about silicon sampling. The motivating idea is simple. LLMs have passed the Turing Test and are hence indistinguishable from people. So if we need to do some sort of measurement or experiment or forecast that involves talking to people, we can query LLMs instead. I scoffed at him: there can’t be people who take this seriously, can there? He laughed at my naivety. Here we are in 2026, and there are multiple hot startups and hundreds of research papers excited about the promise of silicon samples.

And I’m still confused why anyone thinks this is a good idea! But we’re going to spend a class period trying to figure it out. My impression is that quantitative social science is also confused, and this could be another example of AI doing what AI does best: forcing us to reckon with whether our disciplinary practices have been asking the right questions in the first place.

Our lectures on polling brought up a critical tension: Are polls measurements or forecasts? A measurement must be tied to some construct that exists and can be quantified. A forecast predicts some quantitative outcome that has not happened yet. “The percentage of likely voters who would vote for candidate X today” is much less real than “the count of ballots for candidate X.” Trying to predict a hard quantifiable object is very very different from trying to estimate a fuzzy psychological aggregate.

If you are trying to do prediction, there’s nothing wrong with modeling. No one says you need to talk to people to predict the outcome of an election. Indeed, many experts still insist that election outcomes are highly predictable from “fundamentals” like presidential job approval, economic growth, and incumbency.

In fact, as we described last Thursday, even the most committed pollsters use their own bespoke set of “fundamentals” to build predictive models that adjust their poll results. They have to correct for the fact that they can’t collect random samples and they have high response bias. They probably could just use their predictive models and not worry about the polling information at all. This will likely be very predictive of the election outcome, but it is not a measurement.

Now, what does it mean to “measure” public opinion? 100 years after Walter Lippmann, we still don’t have a satisfactory answer. We assume that there is some aggregate percentage of people who agree with some concept, and we measure this by nagging them with carefully worded surveys. While the central limit theorem says we only need to talk to a few hundred random people to estimate a binary response, a survey doesn’t tell us what that binary response means or represents. You need some nomological network to map the complex stuff happening in individuals to a meaningful population aggregate that could be used in policymaking, political campaigns, marketing, or the social scientific understanding of a public.

Here enters the allure of the Silicon sample. If a social scientist has a perfect simulator of people, they have perfect control over experimental conditions and can tweak variables to see how “people” respond. They can change demographics, personal backgrounds, and material conditions. They can create whichever publics they imagine. This lets them perhaps build and test theories of psychology, sociology, and politics without being slowed down by the messy burdens of reality.

Of course, this requires us to believe these “digital twins” are accurate simulations of reality. And I have no idea why we think they’re anything more than the mesmerizing chatbot illusion Weizenbaum called out half a century ago, fleshed out with dozens of generations of Moore’s Law scaling.

There are a bunch of papers that ask a variety of social scientific questions and come out with whatever they want to see. I’ve linked a working bibliography below. I liked the one from Pew, which found that silicon samples and real samples were different. Which one is right, though? Do we trust the answers from the online survey panel?

In these papers, you’ll see the strong prediction/measurement split. For prediction, LLMs are excellent. Just yesterday, Eva Vivalt published new work showing that LLMs can predict the outcomes of randomized controlled trials preregistered in the American Economic Association’s registry and published in 2026 with surprising accuracy. The academic disagreements are all about measurement, interpretation, and construct validity. The construct of a “person with demographics” is weird in and of itself, and these papers can’t figure out what to make of the fact that you can match survey conditional probabilities but find no diversity inside the made-up categories of people. LLMs think all computer science professors in their forties who write a blog respond the same way. But is this a problem with the LLM or the questions fed to the LLM?

I’ll probably come back to this topic in the next lecture blog. I’m excited to see how the students make sense of these papers. I’m also curious whether you, my readers, have read any other papers you found persuasive on this topic. I’m particularly interested in reading the bullish arguments for silicon samples. If you have some good ones, link them in the comments. I’m less interested in the topline results of these papers and more interested in the theory. The bibliography below is a live documentation of social scientists grappling with the purpose of their fields. They’ve yet to reach consensus.

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Working bibliography

1. Lisa P. Argyle et al. (2023). Out of one, many: Using language models to simulate human samples. Political Analysis, 31(3), 337-351. https://doi.org/10.1017/pan.2023.2

2. Joon Sung Park et al. (2024) Generative Agent Simulations of 1,000 People. https://arxiv.org/abs/2411.10109

3. Bisbee, J., Clinton, J. D., Dorff, C., Kenkel, B., & Larson, J. M. (2024). Synthetic replacements for human survey data? The perils of large language models. Political Analysis, 32(4), 401-416. https://doi.org/10.1017/pan.2024.5

4. Jamie Cummins (2025). The threat of analytic flexibility in using large language models to simulate human data: A call to attention. https://arxiv.org/abs/2509.13397

5. Binz, M., Akata, E., Bethge, M. et al. A foundation model to predict and capture human cognition. Nature 644, 1002–1009 (2025). https://doi.org/10.1038/s41586-025-09215-4

6. Athena Chapekis, Arnold Lau, Samuel Bestvater, Sono Shah, Andrew Mercer, and Aaron Smith (2026). Can AI Stand In for Human Survey-Takers? Not Really. Technical Report. Pew Research. https://www.pewresearch.org/data-labs/2026/09/30/can-ai-stand-in-for-human-survey-takers-not-really/

7. Leif Weatherby and Benjamin Recht (2026). This Is What Will Ruin Public Opinion Polling for Good. The New York Times. https://www.nytimes.com/2026/04/06/opinion/ai-polling.html?eafs_enabled=false

8. Jiawei Chen et al. (2026). Towards real-world human behavior simulation: Benchmarking large language models on long-horizon, cross-scenario, heterogeneous behavior traces. arXiv preprint. arXiv:2604.08362.

9. Ashokkumar A, Hewitt L, Ghezae I, Willer R. Large language models can predict the results of social science experiments. Nature. 2026 Aug;656(8126):115-122. doi: 10.1038/s41586-026-10742-x. Epub 2026 Jul 8. PMID: 42420458.

10. Clinton, Joshua et al. (2026). Public Opinion in the Age of AI. APSA Preprints. doi: 10.33774/apsa-2026-1rg21-v5.

11. Eva Vivalt (2026) Can Artificial Intelligence Forecast Treatment Effects in Economics? Technical Report. https://evavivalt.com/papers/Can-AI-Forecast-Treatment-Effects-in-Economics.pdf

12. Ian Hacking (2006). Making Up People. The London Review of Books. Vol. 28 No. 16. https://www.lrb.co.uk/the-paper/v28/n16/ian-hacking/making-up-people

Hi there, argmin readers! Today’s post is a live blog of Class 15 of my graduate seminar “Forecasting: A Critical Retrospective.” In this class we discussed the purpose of election forecasting. The syllabus and list of past posts are here.

We’re a week out from election day, and we all know the Democrats are going to win a bunch of seats. The data team at The Economist has run 25,001 simulations of every House race and aggregated the results into this convenient histogram predicting a 95% chance that the Democrats win the House of Representatives.

They give only a meager 56% chance for the D’s to take the Senate. You can all place your bets now.

The numbers here are based on “national and race-level polls from FiftyPlusOne with fundamental data about past electoral results and the nominees in each contest.” Everything is neatly quantified into some code base to generate bell curves. Next Wednesday, they’ll release a model for 2028.

I’ve spent a lot of time on this blog and elsewhere flummoxed by the influence of this sort of forecasting, and I didn’t leave our class yesterday with a satisfactory explanation. Why do we need to know the outcome of an election before it happens?

We all know this deep down, but the answer seems to primarily be entertainment. Or at least, news posing as entertainment. In the US, polls in news reporting predate their use by campaign strategists by well over half a century. They have always been a fun way to inform readers of the dynamics of our endless presidential campaigns. Since elections are always happening, we comfort ourselves with forecasts that suggest these campaigns matter and are worth the vast amounts of money thrown at them. And since campaigns start the day after election day, polls provide a funnel of endless news content.

Moreover, polls give us an easy way to view politics as sports (a horse race), and sports get eyeballs more easily than policy briefs. Who has momentum? Whose gaffe has tanked their chances? You could even argue that turning elections into a sporting event inspires public engagement. In class, someone recounted an anecdote about only thinking Mamdani had a chance to be NYC mayor once reputable polls measured his growing support.

But there’s no real “score” in elections. It doesn’t matter if you poll well in June if you lose in November. Why do we need to pretend to measure the public’s opinion of how they’d act if an imaginary election were held today? Polls are a beautiful example of the quantification trap, where the numbers make it feel like reporters are being objective when reporting the “score” of the game. This makes them appear more objective than going around and talking to individual people at campaign events or providing other qualitative analyses. The media thinks the public wants a balanced calling of balls and strikes. If you’re just reporting other people’s opinions, you can pretend that you don’t have one.

For that quantification to be trustworthy, the public has to believe the horse-race polls are giving “accurate” scores. If people don’t trust the polls, they’ll stop reading them. A good polling outfit confers institutional prestige on the publication. So you’d better hire good pollsters and poll reporters. This is true in campaigns too: relying on polls keeps pollsters employed, and that gives campaigns one more useless way to spend down their unreasonably massive war chests.

Though forecasters want to be scored using ornately scientific proper scoring rules, they are scored on their most recent track record. They get their prestige through the same path as cephalopods choosing FIFA winners. The history of polling is littered with falls from grace. Literary Digest had decades of strong forecasts with their straw polls until 1936, when Gallup showed them up with modern random sampling techniques. Those sampling techniques whiffed, claiming Dewey would beat Truman. John Zogby was the king of polling in the 1990s, but the industry piled on him when he started missing wildly after switching from random sampling to “interactive polling.” Nate Silver was a media darling after Obama, but his forecasts started crapping out with the election of Trump.

And even if you wanted to properly score presidential election forecasting, it’s a fool’s errand. As Grimmer, Knox, and Westwood have pointed out, there just isn’t enough data to decide who is “best.” The evaluation of pollsters has to be based on calling winners and losers. They have to be judged with recency bias. Polls are infotainment, so they are better evaluated as media properties than as scientific instruments.

Nate Silver thought he had an out by claiming he’s just a humble handicapper. He’s forthright in telling you that he thinks his purpose is helping people bet on election outcomes. And since he said Trump had a chance, you could have made money if you read his reporting. This argument is some civically destructive nonsense, but fortunately everyone who isn’t a degenerate gambler is disgusted when Nate talks that way.

Maybe it’s just me, but I think we’re well past the heyday of the election forecaster. There are still tons of websites with poll aggregates, but these numbers seem to matter less than they used to. People are used to the polls missing bigly. Scammers are putting out fake polls for lols. There has been no successor to Nate Silver because we haven’t figured out what to do next. In class on Thursday, we’re going to talk about silicon sampling. Let’s hope that’s not it.

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Over the past few weeks, I’ve been giving a talk, “The World Is Something We Make,” about truly open language models. I’ve written everything I say in that talk on this blog at one point or another, but I’ve never put all of those thoughts in one post. Given that Anthropic S-1 was just released, with them beckoning us to submit to their unstoppable momentum, it felt worth reminding myself and you, my readers, that there is clearly another way forward and that no future is inevitable.

In 2024, David Donoho wrote a compelling essay, “Data Science at the Singularity,” arguing that the superpowers behind advances in AI were the engineering and research practice. The community encouraged what Donoho dubbed “frictionless reproducibility,” a culture of shared tasks, code, and benchmarks. People worked on a shared suite of datasets. They engaged in (mostly friendly) open competition to show who could be best. But most importantly, they made their processes, procedures, and code open.

This open process not only improved performance on the shared benchmarks. It also bred remarkable innovations, including code optimization and acceleration, generalization to new problem domains, opening the field to more engineers and stakeholders, and transparent processes that allowed reasonable auditing of the technology.

You can trace this pattern linking openness and innovation all the way back to digit recognition at Bell Labs in the 1960s.1 Indeed, you might argue that the AI Winters happen precisely when people stop sharing benchmarks and tasks. Over the past twenty years, frictionless reproducibility has reshaped how we build recommendation systems, classify images, and think about language. It even led to a Nobel Prize in chemistry, with protein structure prediction effectively being solved through the pathway of frictionless reproducibility.

Unfortunately, with the rise of large language models, the machine learning community took a hard 180 into a world of consolidated, closed development. The original sin of the language model was using training data acquired illegally. Even though the companies maintain this is all fair use, they clearly don’t believe it because they refused to tell everyone else what data they used for training. This quickly became an excuse to close off research, justified by specious arguments about capitalist competition and fantastical stories about sci-fi safety.

The end state we’re in today is reprehensible. On the one hand, machine learning technology is more amazing than I ever imagined it could be. On the other hand, it’s a technology making everyone miserable. Knowledge workers drive themselves insane in a flow state with their stochastic productivity software. Data centers are less popular than coal plants. And the broader community outside of the umbrella of creatively financed venture spending can’t take back control because small innovations on small models have no relevance or impact.

So what is our path back to openness? Open weight models are a nice first step. At least they introduce low-cost competition to the market. If you haven’t found a way to run an open model in an open harness and see that it’s probably good enough for 99% of your work, you are very much missing out! But they aren’t really open, are they? As the open software community will attest, if someone gave you an exe file to run, you wouldn’t consider that open. Moreover, the competitive open-weight models are all Chinese, which raises many trust issues for many developers. No, open must mean everything open. That means open weights, code, data, and process. To the best of my knowledge, only two initiatives, Marin and AI2, are committed to this kind of truly open development. They are heroic, but vastly under-resourced.

My question to everyone reading this is simple: how do we collectively commit to building this sort of open infrastructure? Open from top to bottom.

My Berkeley colleague Ion Stoica pithily laid out the three necessary components of any large AI project: people, data, and compute. In talking to people over the last few months, I know there is no shortage of people who want to help build truly open language models. Open efforts like Marin, AI2, and, to some extent, NVIDIA, have compelling stories about how we can build training datasets without theft and copyright violations. Sure, there are still unknowns about post-training data, but I’m sure we can make progress on that out in the open too. The hard one, as far as I can tell, is compute. We need a massive collaboration to donate, harvest, and share idle compute. That will require more creativity, but this is creativity about collaboration, not technology. We have the technology to do it. We just need to figure out the right architecture of participation to grow a system bigger than the sum of its parts.

The history of machine learning shows that once we have an open prototype, the floodgates open. Imagine we had a truly open model as good as Opus 4.5. In months, the open software and machine learning communities will have figured out how to train this 1000x more efficiently. They will have figured out ways to fine-tune it to specific tasks and domains. And they will have audited its guts to understand how to deploy it safely and securely. But this is all predicated on having the open prototype so we can collaborate.

I don’t think it’s absurd to imagine such a prototype existing. We just need a bit of organization to put this effort together. The title of this post is a quote from David Graeber, who wrote, “The ultimate hidden truth of the world is that it is something that we make, and could just as easily make differently.” No future is inevitable. Cheers to that.

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Hi there, argmin readers! Today’s post is a live blog of Class 14 of my graduate seminar “Forecasting: A Critical Retrospective,” turning to the less controversial subject of public opinion polling. The syllabus and list of past posts are here.

Our next two units on forecasting focus on forecasting societal behavior, and to do that we first need to talk about how we measure properties of society. One of those main measurements is surveys. Today, I want to describe some techniques survey designers use to avoid ever having to interact with actual people.

Let’s start with the basics.1 Let’s say you want to measure some property of a population, like what percentage of dentists recommend chewing sugarless gum. You can’t ask all of the dentists, so you gather a random sample and then extrapolate the fraction in the sample to represent the fraction in the broader population of dentists.

The main idea of why this is reasonable is simple. If you gathered a true random subset of a population of people and asked them a yes-or-no question, then the average of the answers in the sample would most of the time be very close to the average in the population. You can even quantify how close. The expected gap between the sample average and the population average is nearly independent of the population size and mostly a function of the sample size. This gap is inversely proportional to the square root of the sample size, so if you want to estimate the fraction of a population that answers yes to some question, you can get a “margin of error” of a few percentage points with a few hundred people.

This is a colloquial description of the weak law of large numbers. It often feels miraculous. You can get a good estimate of an average with 600 samples no matter how large the population is. But that margin of error is only true if you have a truly random sample. Unfortunately, when you’re harassing people to answer your annoying surveys, you never get a truly random sample! Not everyone will talk to a pollster, and not everyone is reachable in the first place.

So the data that surveyors gather is a mix of randomness, convenience, and population predilections. You can’t just average the responses and hope for the best. Without a truly random sample, that average will be biased. Fortunately or unfortunately, statisticians have spent decades finding clever ways to use math to patch up social scientific deficiencies. They don’t let people’s actual behavior get in the way of a good time!

One idea is to use post-stratification to recalibrate your survey. The idea behind post-stratification is that once you have a fine enough demographic coarse-graining of people, there are no systematic biases in reporting. There are many justifications for this assumption, but more or less it assumes that within each demographic unit, respondents vote like nonrespondents.2 If this is true, you can weight the respondents in your sample by their demographic proportion in the population and combine them into a new estimate that is unbiased, assuming your model relating demography and human behavior is correct. My friends Avi, Eli, and Erin wrote a clear introduction to how this is done in practice and what assumptions have to hold for this reweighting to be unbiased.

Now those demographic weights themselves are also hard to come by. First, you need an accurate census to guess the fraction of the population that belongs to each demographic cell. This creates a problem of turtles all the way down, because it requires doing censuses that have similar response and bias issues. Second, you need to be sure that you actually sample someone from every demographic stratum in your survey. That is almost never true.

So what you do instead is fit the weights in your sample using a statistical prediction model. There are many dark-art techniques to do this, each with its own ornate justifications. Fitting the weights gives modelers a lot of degrees of freedom. Pollsters are now using their own internal models to weight their numbers. Different models can cause swings in estimates far outside the “margin of error” reported with the poll.

This is only one way statistical prediction blurs into statistical sampling. Indeed, you can lower the variance of your survey with a good prediction. In classical survey calibration, you combine your model’s guess of the outcome with the estimated deviation from that model in your survey sample. In this paradigm, if you really believe in your prediction model, you can throw the survey correction out altogether.

If you want to boost your confidence, you can even combine these two prediction techniques. Statisticians hilariously call this “doubly robust.” If the model that predicts poll answers from demographics is correct, the term that depends on the sample data will be small and not mess up your prediction. If the model that predicts who will be in the sample based on demographics is correct, this will cancel out the effect of the answer-predicting function. Unfortunately, some guy told me that all models were wrong. In that case, there are no guarantees.

Regardless, my point here is to show how statistical modeling can replace statistical sampling. As more and more people refuse to answer polls, these statistical models end up replacing talking to people. In practice, surveys become more about what experts believe about society than what society actually is. Many of these experts seem to believe that they can forecast human behavior without ever observing humans.

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Hi there, argmin readers! Today’s post is a live blog of Class 13 of my graduate seminar “Forecasting: A Critical Retrospective,” in which we touched the third rail of forecasting discourse: pandemic modeling. The syllabus and list of past posts are here.

No forecast had a greater impact on our lives than “Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand.” Written by epidemiologist Neil Ferguson and colleagues, the report presented prefactual scenarios of what would happen in the UK and the US under various pandemic mitigation strategies. Report 9 was released on March 16, 2020, and many nations and states soon heeded its advice, closing schools and businesses and mandating that citizens lock themselves in their houses.

The report estimated the death tolls—without error bars—for three potential policy scenarios. Doing nothing would lead to 510,000 deaths in the UK. Enacting a “mitigation” policy, where symptomatic people isolated at home and people at risk practiced “social distancing,” would lead to 250,000 deaths. Most optimistically, following the lead of China and enacting a policy of “suppression”—an aggressive, authoritarian shutdown of society—would “flatten the curve” and lead to only 20,000 deaths.

These numbers came from a complex computer simulation with over 900 parameters, almost all of which were unknown. Despite this tremendous uncertainty, the report concluded that “epidemic suppression is the only viable strategy at the current time.”

Even at the time, it was clear that Report 9 was more an advocacy document than a scientific report. Report 9 provided a scenario under which a better future, under a completely untried and untested policy, was possible. Unfortunately, that better future didn’t manifest itself, and faith in public health agencies and other decision-making institutions has never recovered. The team leaned on its institutionally approved scientific expertise to sway public opinion. This was a major risk, and, in retrospect, I wonder if the broader public health community thinks it was worth it.

I don’t want to litigate pandemic policies today, but we can’t talk about what forecasting does without talking about Report 9. It has all the hallmarks of a bad forecast. Its authors used a complex model to produce concrete numbers with no qualification of the tremendous uncertainty in their numbers. They didn’t share their baroque model with the public for over a month. Once it was released, others showed the model itself only shakily supported its own findings. Indeed, Edeling et al. showed that under a mild sensitivity analysis, the 20,000-deaths forecast was at the lower boundary of the 68% confidence interval, well below the mean forecast. It’s as if the team chose parameters to make their policy look as good as possible.

Moreover, the team refused to estimate any of the impacts of their policies beyond burden on the health system and deaths. Report 9 wrote, “while experience in China and now South Korea show that suppression is possible in the short term, it remains to be seen whether it is possible long-term, and whether the social and economic costs of the interventions adopted thus far can be reduced.” They had only a single sentence estimating these costs: “The social and economic effects of the measures which are needed to achieve this policy goal will be profound.” They claimed estimating these social impacts, whether on educational outcomes or economic output, was outside their expertise. Many interpreted this as the team asserting these outcomes were not ethically significant enough to even attempt to model.

As the pandemic progressed, it became apparent that the epidemiology community was bad at short-term forecasting. Human pandemics had basic rise-and-fall shapes predicted by elementary compartment models (known as SIR models), but when they would rise and peak was much harder to guess than Report 9 suggested. Indeed, recent work by White and Leon suggests that overconfidence in forecasts comes from trends that are easy to spot: seasonal trends, statistical smoothing, and exponential growth make pandemics easy to predict. Without these features, disease impact is impossible to predict. Scoring rules paper over the fact that we mostly have no idea how to forecast these things. We all learned in real time that epidemiological tools have very little predictive power. They are, at best, descriptive. And yet we were told in March 2020 to trust their long-term forecasting.

The actual death toll in the UK was later estimated to be around 230,000. Whatever the actual number is, the consensus is that it is much, much larger than 20,000. As is always the case when a forecast doesn’t pan out, the forecasters can argue there is no true Scotsman. They might say the policy was poorly implemented and the disease would have gone away if we had acted better. Such arguments carry no water in medicine, and they shouldn’t carry water here. A medical intervention is only effective if a patient population is willing to take it. A real population isn’t what you wish it would be. None of the proposed non-pharmaceutical interventions stopped the eventual wave of disease anywhere on earth, even in China.

Whether the suppression strategy worked is unknowable. We know that more than twenty thousand people died. We don’t know how many would have died under a different policy. We can’t know what the economic and educational outcomes would have been under a different policy either.

What exactly can we conclude then? A while back, I wrote about the Y2K bug and the preparedness paradox and latched onto John Quiggin’s argument that there were multiple true interpretations of the decision making. The COVID pandemic brought a similar pattern of simultaneous truths. It’s true that many people suffered and died, and some were saved by avoiding contact with others. It’s true that we overreacted and harmed children’s education and socialization. It’s true that “the other side” promoted plenty of craziness (Ivermectin? Hydroxychloroquine? Injected bleach?). I could make a long list of truths that would logically contradict each other.

But it’s also true that no one was able to predict the future. It’s obvious in retrospect, but questions of what should be normalized are questions of values, not data science. And in most political decisions, values have to trump science and its messy uncertainty. COVID forced us to make massively consequential decisions in the face of massive uncertainty. We used numerical reports and forecasts to dodge the moral consequences of our actions.

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Hi there, argmin readers! Today’s post is a live blog of Class 12 of my graduate seminar “Forecasting: A Critical Retrospective.” The syllabus and list of past posts are here. It might also be a subtweet of yesterday’s AI discourse?

Twenty-five years ago, Leo Breiman wrote a prophetic warning to his statistical brethren:

“There are two cultures in the use of statistical modeling to reach conclusions from data. One assumes that the data are generated by a given stochastic data model. The other uses algorithmic models and treats the data mechanism as unknown. The statistical community has been committed to the almost exclusive use of data models. This commitment has led to irrelevant theory, questionable conclusions, and has kept statisticians from working on a large range of interesting current problems. Algorithmic modeling, both in theory and practice, has developed rapidly in fields outside statistics. It can be used both on large complex data sets and as a more accurate and informative alternative to data modeling on smaller data sets. If our goal as a field is to use data to solve problems, then we need to move away from exclusive dependence on data models and adopt a more diverse set of tools.”

Breiman saw that prediction was at the heart of most of his consulting projects. Rather than being asked to determine causation, he was asked to make forecasts. His list of examples is instructive:

• Predicting next-day ozone levels.

• Using mass spectra to identify halogen-containing compounds.

• Predicting the class of a ship from high altitude radar returns.

• Using sonar returns to predict the class of a submarine.

• Identity of hand-sent Morse Code.

• Toxicity of chemicals.

• Online prediction of the cause of a freeway traffic breakdown.

• Speech recognition.

• The sources of delay in criminal trials in state court systems.

If you asked anyone today how they’d solve these tasks, they’d say “collect data and fit a neural net.” You had to be there at the time, but this was quite controversial in 2001. Indeed, even using a decision tree was controversial. Many people thought models built with expert knowledge, with meaningful parameters fit to data, would be far superior for prediction. Moreover, you’d be able to interpret your predictions because you had a mechanistic understanding of reality encoded your predictive stochastic data model.

Given what’s happened since, I don’t think anyone needs convincing that neural nets will work better. Indeed, the reaction in class yesterday confirmed that the zeitgeist has shifted 180 degrees. Of course you’d rather use a neural network than a complicated model. For all of those tasks, everyone would say “use a transformer or do in-context learning and forget about it.” Autoregression has won out by brute force.

Now, given my long history as a machine learning researcher, I don’t think you’ll be surprised to find that I agree with Breiman and struggle to justify stochastic models. However, I think I can capture the motivation of modelers: people want more from their models than predictions.

People like mathematical models because we think that understanding how something works from top to bottom lets us better predict how it will behave in the future. A mechanistic understanding not only lets us play out likely futures, but lets us imagine what might happen under a variety of different adversarial scenarios. These models assure us that we understand the present well, because we can point at all of the subcomponents and build a bottom-up description of macroscale behavior.

It’s so weird how our forecasting culture turns this around: IF we can make good predictions, THEN we understand. You present your Brier Score first. Only if it tops the prediction-market leaderboard are people impressed enough to go read your 25,000-word description of how you prognosticate. Accepting this logical inversion—that accurate predictions indicate understanding—is why our rational brethren venerate superforecasters. But it’s clear that even the most committed forecast bros don’t like this, because they also obsess about mechanistic interpretability.

But when we seek explanations, all we have is the data from which our predictions are made. Data-driven modeling is implicit, leaning on the tacit knowledge of what makes good data and what makes bad data. Almost everything you want to interpret lies in the data and your optimization objective. The compressed storage that are the parameters of your nonparametric model hold this information too, but reading the tea leaves of the weights is like trying to understand a book by looking at the bits in its zip file.

In a wholly data-driven world, better understanding can only come from getting new data. We can either wait for the future to roll in, or we can act to get that data now. That is, to rapidly understand the world you forecast, you have to be able to do things. You need to intervene and act to rule out explanations. This is experimentation.

Forecasts alone are not experimentation. Indeed, a recurring theme in this class is how passive forecasting is. Focusing so hard on prediction makes us forget we can take actions to change the future.

Some think that predictions can shape the world. By warning people of doom, perhaps someone out there will take action. And yet, my impression is that the most dedicated forecasters think their best available action is to place bets. Or write open letters. Abandoning their agency makes their prophecies self-fulfilling.

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Hi there, argmin readers! Today’s post looks at part of OpenAI’s math repository that claims to compute faster Fourier transforms. It’s more technical than usual, but I tried to add some tutorial material for people who need a refresher course on signal processing or computational complexity.

The Fast Fourier Transform is one of the most important innovations in digital signal processing and one of my favorite algorithms. The FFT is a fast way to extract the frequency content of signals, letting you rapidly analyze, filter, and manipulate frequencies across different bands of the spectrum.

The Fourier transform computes the energy in each frequency band through a simple dot product.1 Let x denote your input, a length n array of samples, and f a frequency. Then the amount of frequency content in x at f can be computed by the formula:

For digital signals, a bit of math shows you only need to compute n of these dot products, one at each multiple of the frequency 2𝜋/n, to understand all of the frequency content. Naively, this requires n multiplications and additions for each frequency. Hence, computing the entire Fourier transform appears to require n² arithmetic operations.

The fast Fourier transform is a clever recursive procedure devised by James Cooley and John Tukey in 1965.2 The main idea is that a length-n Fourier transform can be computed by shuffling the input vector, computing two Fourier transforms of length n/2 on the shuffled components, and then recombining the outputs using atomic arithmetic operations. The shuffles and recombinations take a linear number of arithmetic operations. Repeating this procedure iteratively, namely, log₂(n) times, computes the full discrete Fourier transform. With the bookkeeping, the FFT computes a length-n Fourier transform in fewer than 5 n log2 n arithmetic operations.

To make this acceleration concrete, when n is 1,000, n^2 is 1,000,000 and 5 * n log n is around 50,000, a 20-fold speedup. When n is 1,000,000, the speedup is 10,000-fold. These speedups can be the difference between a transform being computable or not given the constraints of a signal processing application.

Since the invention of the FFT, people have looked for even faster Fourier transforms. One question is just how fast you can go. It seems like you probably need at least n operations to compute the FFT, as it takes n steps just to write it down. The FFT is 5*log₂(n) times slower than that reasonable speed limit, and that 5*log₂(n) factor can be big. It’s 200 when n is a trillion. Can you do something clever to reduce that prefactor of 200?

Well, lo and behold, in the massive paper dump OpenAI took on the mathematics world last week, they claim to have a faster Fourier transform. The main claim from their discriminatively named “main.pdf” is

I was intrigued about what was going on here. The log(n) term, in theory, was a teeny tiny bit smaller than in the standard FFT.

Did I read this paper? Of course not. No one at OpenAI read this paper either, so why should I? I did what every other mathematician in the world does with AI slop mathematics: I fed it back into the slop machine and ran an information retrieval session with a chatbot interface to extract salient facts. Anthropomorphically speaking: I asked ChatGPT what it thinks about its own output. This is how we do mathematical research now. What a world.

Unfortunately, I did not find a faster Fourier transform. Instead, I found the rot that develops inside applied mathematical theory when formalism becomes so detached from reality that a “breakthrough” is nothing more than an artifact of mathematicians not being able to properly specify the rules of their games in natural language.

First, “big-O” notation has been so abused that it has become meaningless. Let’s review the definition, which impressed me as an undergrad. An algorithm has running time T(n) = O(F(n)) if there exists an integer N and a constant C such that

That is, the number of steps the algorithm actually takes is upper bounded by a constant times some convenient function F(n) as long as n is large. F(n) is usually something familiar and interpretable, like a polynomial or exponential function. This notation says that we only care about what happens when the size of the computation is large. We care about the asymptotic growth rate of the computation time. All constants are equivalent.

Big-O notation is useful for shortcuts in algorithmic accounting, but it also allows for remarkable logical laziness. If we want a practically faster FFT, we want an algorithm that requires fewer than 50n operations for reasonably sized n. But O(n) does not mean 50 n. It could mean 10⁸⁰ n. This would be considered a “linear time” algorithm. An algorithm that requires n + 10⁸⁰ is also considered a linear time algorithm in the big-O regime. An algorithm that only has linear-time guarantees when n is greater than 10⁸⁰ is also considered linear time. 10⁸⁰ is approximately equal to the number of atoms in the known universe. That is why Richard Lipton and Ken Regan call algorithms with unfathomably large hidden constants galactic algorithms.

The OpenAI FFT algorithm is definitely galactic. The estimated values for C were 10¹⁰⁰ when N=10¹². So even when n=10¹⁰⁰, the venerable Cooley-Tukey-Gauss FFT would be 10⁹⁹ times faster.

So why is this new FFT result interesting? Well, note that in big-O notation, it is technically asymptotically faster than the Cooley-Tukey algorithm because

I mean, sure. But given the constants, the algorithm runs faster only when n is impossibly large. Roughly, you need

whatever the hell that number means.

Lipton and Regan argue galactic algorithms are useful because they spur research. Once you show a running time is asymptotically possible, you can spend your time finding an algorithm that practically achieves this provable running time. Maybe you can send your AI agent swarms after it. You do you. Maybe you can get a practical algorithm out, but I don’t know of any legitimate examples where this happened. I’m particularly doubtful here, because the model of “computation” OpenAI uses bears no resemblance to an actual computer.

“The model uses exact complex arithmetic.” That means it assumes you can store and multiply complex numbers at arbitrary precision. Indeed, the algorithm requires you to multiply complex numbers whose magnitudes grow superpolynomially with n. If you stored these numbers as bits, the memory requirement would effectively be exponential in the input length. It assumes you can multiply such arbitrarily large complex numbers together in a single operation. We do not have computers that can do this. So even if this theorem in main.pdf is “true” (no one knows, and I don’t care), it’s not actually solving the problem we set out to solve when looking for a faster FFT.

For people familiar with theoretical analyses of the FFT, that you need an absurd model of computation to break the FFT speed limit isn’t surprising. In 1973, Jacques Morgenstern proved that you couldn’t get a Fourier transform faster than ½ n log n if you required that complex coefficients used in the computation had bounded magnitude. That should have been the end of the story! But it wasn’t. People said Morgenstern’s restricted coefficient model was too restrictive. Forty years later, Nir Ailon showed that you couldn’t compute an FFT faster than n log n without severe numerical instabilities. This was also too restrictive for some people, I guess.

This new OpenAI result is thus less a mathematical breakthrough and more an oddity of computer scientists being bad at formalizing their design specifications. The “theoretical” definition of a computer is very far removed from the computers we actually build. The “faster” Fourier transform is merely an example where theory gets so unmoored from the original question that an “open problem” becomes nothing more than an academic status puzzle. The solution is like what happens when you set computational bot streams at impossible problems and find them engaging in illegal hacking.

Many of the other “big” results in this OpenAI slopository could be critiqued in the same way. For example, one of those results was a galactic algorithm to multiply two matrices in O(n^2.25) operations. The construction used in the paper does not let you even estimate the constant that hides inside big O.3 It may as well be infinite, computable only with the divine music of the spheres.

Still, if written substantially better, these papers would have made it into the most prestigious publication venues for the theory of computer science (i.e., refereed conference proceedings from STOC or FOCS).4 The matrix multiplication paper would have likely won awards. But neither of these has anything to do with computers!

This is because the theory of computer science has a culture that actively discourages running algorithms on a computer. It’s acceptable to write papers in theory conferences that assert an algorithm exists without ever writing it down. The theory of computer science has become a form of mathematics that doesn’t concern itself with computers, and it offers little reward for impact outside those mathematical pursuits. I explained this to a friend who remarked to me that “theory” has the transdisciplinary meaning of “hiding in obscurity of one’s own making.”

AI is really good at automating our worst tendencies. It amplifies the unspoken cultural practices no one likes, but no individual can reasonably deviate from. It exploits the mechanized traditions recalcitrant to collective action. In that vein, AI can now write useless theory papers. But perhaps in the absurdity of the distasteful OpenAI trash dump of proofs, we can all look up and realize together that we should consider doing something else.

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Hi there, argmin readers! Today’s post is a live blog of Class 11 of my graduate seminar “Forecasting: A Critical Retrospective.” The syllabus and list of past posts are here.

In “Communicating Uncertainty in Policy Analysis,” Charles Manski takes to the Proceedings of the National Academy of Sciences to chastise government officials for their failure to report uncertainty in their forecasts. Now, what would that reporting look like? We need the uncertainty reports to be clear, legible, and objective. Being good bureaucrats, those desiderata tell us we need to quantify our uncertainty.

Sadly, our technocratic imagination for what uncertainty quantification means is woefully narrow. Uncertainty quantification almost exclusively means error bars. In this case of forecasts, an error bar specifically means a prediction interval. A prediction interval is a probabilistic object. It quantizes a forecast of some numerical quantity into a discrete binary event. Rather than saying I think GDP will grow by 3% in the first quarter of 2027, I say, “The chance that GDP will grow between 0 and 7% in the first quarter of 2027 is 95%.” Based on your modeling, you believe some measurement will lie in some band with some probability.

Even our methods to construct these prediction intervals lack creativity. 95% of the time, we build those intervals by assuming the data is Gaussian, estimating the variance, and then setting the bounds to be plus or minus two sigma. That variance estimate might come from direct analysis of the model. For example, if you assume linear dynamics perturbed by Gaussian shocks, you can compute the variance exactly.

For more complicated models, you might get the variance from Monte Carlo simulation or estimate it from past data. For example, in weather forecasting, you could generate error bars by sampling a bunch of likely atmospheric states, propagating them through a complex simulation, and then computing quantiles. Other methods bin past prediction errors, arguing that this isolates aleatoric uncertainty from epistemic uncertainty, then build error bars from those so-called “innovations.”1 If you want to be really fancy and pretend you are avoiding assumptions about distributions, you can just compute 95% quantiles directly from the observed errors.

And that’s more or less all of the tricks we know. How many classes must we spend on it? How many papers must we write about it?2 In this class, we’ll only use one.

I’m always left with the uncomfortable problem that I have no idea what to do with probabilistic error bars. Usually what “probability” means is incredibly sloppily specified in these models. Even in the constructions I described above, the probability is dependent on an unverifiable chain of modeling decisions, and there’s no way to doubly quantify the uncertainty in my modeling. A good engineer will just multiply their error bars by 2 and call it a day.

For better or for worse, however, forecasters are not always engineers. They just might want to use the uncertainty to hedge their bets. If they turn their numerical estimate into a probabilistic one, they can’t be wrong. Conveniently, probabilistic predictions of binary events are more easily scored by our standard proper scoring rules.

Outside narrow forecasting contests, it’s unclear how reporting an interval changes policy decisions. In weather forecasting, you can give people a sense of whether they should bring an umbrella. But error bars on growth are harder to parse from a decision-theoretic standpoint. Yet these are, perhaps unsurprisingly, exactly the sorts of uncertainty reports Manski calls for:

“For example, the CBO could report the 0.10 and 0.90 quantiles of the distribution of potential outcomes that it referenced when scoring the American Health Care Act of 2017. Alternately, it could present a full probabilistic forecast in a graphical fan chart, such as the Bank of England uses to predict GDP growth (see the discussion later in this article).”

Perhaps you can say that all that matters is the sign of GDP growth: negative growth is bad, and positive growth is good. This leads to a self-fulfilling prophecy in macroeconomic planning. When they estimate a negative number, economists declare a recession, and everyone gets mad. The problem, of course, is that many countries have positive GDP growth right now, and people are still pissed off. Making policy where their forecast sign is correct didn’t solve the current administration’s political problems.

Anyway, I’ve written about my disdain for this blindered approach to uncertainty quantification before, and every time I come back to how we always want something else. People want a prefactual analysis for what we should do if our story is wrong. They want to know how we will recover from failures, and articulating the vast complexity of uncertainty might help with such preparation. Halfway through this class on forecasting, my knee-jerk conclusion is that these are what most serious forecasters want too! In Manski’s long list of sources of uncertainty, only a couple can be quantified. However, holistic reporting of uncertainty can prepare us for what the model doesn’t say and help us think about what to do when our forecasts inevitably miss the mark.

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Hi there, argmin readers! Today’s post is a live blog of Class 10 of my graduate seminar “Forecasting: A Critical Retrospective.” The syllabus and list of past posts are here.

All of my cybernetically inclined friends are into Friedrich Hayek, but my research and teaching keep bringing me back to John Maynard Keynes. These two gentlemen occupy the two poles of the dialectic of the American Experiment. Hayek famously introduced the notion of markets as distributed computers, where prices carry knowledge across the economy. Keynes, with his economic theory of central banking, set the stage for centralized computing of economic variables to govern those markets.

In Keynes’ paradigm-shifting 1936 work, The General Theory of Employment, Interest, and Money, he lays out an oxymoronic formula for central planning in capitalist societies.1 The basics of the Keynesian model are laid out in the appendix of Robert Evans’ paper from this week’s reading. The national economy has four key variables: the amount of investment firms make into the economy, the amount of savings firms accumulate in financial instruments or by paying down debt, the demand for money in the economy to facilitate purchases and sales, and the supply of money from the government. To change these variables, the government can enact various policies. For example, it can invest in infrastructure, raise taxes, increase the money supply, or change interest rates. Keynes argues that the government can dictate the economy’s output—and hence the general welfare of all citizens, who are players in the big macroeconomic game—by properly executing its policy apparatus.

This would set the stage for the subsequent 90 years of democratic capitalist monetary policy. The government has to make policy to ensure a well-run economy. To do this, it has to know the current state of national investment and savings. It also has to be able to forecast what these variables will be if no policy changes are enacted. This last requirement has driven the major investment in macroeconomic forecasting.

Forecasting in macroeconomics is thus primarily a tool of control. Here I mean control in the academic sense: the theory of dynamical systems with inputs and outputs and the design of subsystems to drive outputs to desired targets. Keynes casts the economy as a giant control problem, where the goal is to deftly change policy to ensure a particular state of economic output and employment. It should be no surprise that tools from control, notably the work of Rudolf Kalman on optimal filtering and control of linear systems with quadratic objectives, play a central role in macroeconomics.

Now, to filter and control, we need to make predictions. Keynes didn’t tell us how to generate those predictions. But his disciples, in what is often called “Keynesian” macroeconomic forecasting, write down structural equations of the economy, fit the parameters of these equations using varied means, and then make forecasts directly from the fitted models.

This program of prediction ran into several obstacles. First, it requires mathematical equations that predict all of the aspects of the economy needed to precisely determine optimal policies. Second, it requires a massive measurement system to pin down all the relevant factors in the model. Both were terribly daunting and required a great deal of expert judgment.

Economists want their methods to be “scientific,” since they influence decisions with major consequences. However, with so many variables, so little stationarity in economic conditions, and so much politics involved, building a truly objective and replicable system seems like a fool’s errand. Beatrice Cherrier details some of the typically arbitrary, political nature of macroeconomic sausage-making in this blog post. Evans details the amount of analytical flexibility and expert judgment forecasters necessarily employ in their predictive techniques.

Beyond these nuances of modeling and measurement, however, a fundamental problem of feedback control remains insurmountable. The models have a ton of parameters that are fit to historical data. Different policies yield different parameters. These parameters change when a policy changes. And you can’t predict what the parameters will be after a policy changes. So what on earth are we doing?

The critique in the previous paragraph was levied at macroeconomic forecasting by Robert Lucas in 1976. That macroeconomic forecasting is still an influential practice 50 years later certainly tells us something. Macroeconomic forecasters occupied positions of power and held a sense of civic duty. So they took Lucas’ critique as a challenge, not a reason to close up shop.

I’m not going to hash out the various attempts to build complex, nonparametric macroeconomic models that add ornate complexity while failing to dodge the fundamental problem. Theoretical critiques can carry only so much weight. The fact that the Great Recession was substantially caused by terrible financial policy and inadequate forecasting should have been the nail in the coffin. In 2003, Robert Lucas himself declared that macroeconomics had been a great success:

“My thesis in this lecture is that macroeconomics in this original sense has succeeded: Its central problem of depression prevention has been solved, for all practical purposes, and has in fact been solved for many decades.”

Oops.

Economists didn’t see a problem with the deep instability created by hyperfinancialization. Indeed, though Evans did his ethnographic research on macroeconomists a decade before the crash, his point rings true:

“...[E]conomic policy cannot be based on a quantitative calculus of costs and benefits and must, instead, rest on the considered judgement of a community of experts. Macroeconomic modellers may be those experts, but to expect anything more from them is to expect too much.”

So who should we trust? The Obama administration hoped economists could help get us out of the mess. But 8 years of attempted neoliberal patching of the American system ended in such broad dissatisfaction that… well, you know what happened. We’ve since had a decade of federal unrest as we try to unmoor ourselves from the expertise of economists. While I don’t believe the Biden and Trump administrations have found themselves a suitable alternative, I make no predictions about whose policy advice we’ll be deferring ot next.

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Hi there, argmin readers! Today’s post is a live blog of Class 9 of my graduate seminar “Forecasting: A Critical Retrospective.” The syllabus and list of past posts are here.

Every class I teach seems to require a lecture or two on expected utility maximization. It’s the basis of classification rules, so it’s integral to machine learning classes. It’s the simplest stochastic optimization problem, so it appears in my optimization classes. It’s a great motivator for probabilistic thinking, so it appears in probability classes. Perhaps a bit less well appreciated, it’s an indirect proper scoring rule for forecasts, so we have to talk about it in this class. And, I suppose, it’s a mathematical tool that scarily dominates the philosophy of many powerful people in government and industry alike. It’s worth understanding the nuts and bolts!

Part of what makes utility maximization so appealing is how simple the core idea is. We want to decide whether to act or not. We build a probabilistic model of the world under the action and compute the expected value of the benefit. We also build a model for what would happen if we don’t act and compute the expected value of the benefit of inaction. We choose to act if our calculations imply that action has more benefit than inaction.

What could be simpler? You compute probabilities. You compute costs. You multiply them together and add them up. Everything is beautifully quantified and calculable.

The only problem is these numbers are all made up. They are forecasts, and they are rarely justifiable. Outside of the casino, we rarely know how to calculate precise odds of outcomes. Worse, forecasting the prices out in the future is also inherently uncertain, often more uncertain than the odds calculations. Maximizing the utility of a rational actor or a general population is an appealing philosophical goal, but the precise rational calculations are always made about fantasy stories. Economists know this, and proceed with caution. In the comments of Tuesday’s post, Jordan Ellenberg flagged this quote from John Maynard Keynes.

“By ‘uncertain’ knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty… Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealthowners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed.”

Keynes here seems to be reluctantly defending utility maximization as the best of many bad options for decision making in the face of uncertainty. But I don’t think that’s his point at all! Keynes is defending his “General Theory of Employment” and arguing against this sort of utilitarian calculation.

As it is colloquially known, “Keynesian economics” — a term that sadly oversimplifies Keynes’ brilliant collected works — tells governments to stimulate economies during recessions. Keynes argues that we can’t accurately predict the future, and hence people tend to lean on status-quo bias. The safest bet is to assume nothing changes. But when the status quo is bad, people become risk-averse and hold their money. This hoarding prolongs recessions. Because the future is uncertain, people don’t act “rationally” when they fear they might not have money to spend later. Keynes thus argues that governments should step in to nudge citizens out of their undue pessimism by giving them extra money to spend.

Written in the pits of the Great Depression, Keynes’ argument in his 1937 article in the Quarterly Journal of Economics articulates how utility maximization goes wrong. The future is unknowable. Uncertainty makes people afraid. Fear makes hoarding more attractive. Mass hoarding perpetuates a vicious cycle of societal hardship. At this point, someone needs to step in to get the ball rolling, eating up some of the risk to inspire more confidence in people to spend their money.

In this class, we’re not going to debate the merits and challenges of recessionary stimulus spending. But Keynes’ article (which I have added to the reading list) articulates the nuance of forecasting under great uncertainty. Human psychology plays a key role. Today we’ll go through how this appears in the mathematics, with different utility functions expressing different models of risk aversion, and different algorithms for action. We’ll see that not only are the costs and benefits uncertain, but the algorithm itself can be shaped by different models of psychology. Expected utility maximization might be a reasonable way to engineer machines, but it’s not something that reasonable people do. Understanding the many hyperparameters of optimal decision making can help us better understand the psychology of people obsessed with forecasting.

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Hi there, argmin readers! Today brings one of my polarizing football posts. But it is nicely timed with the classes on cost-benefit analysis!

Football season is well underway, and my favorite absurd sports-analytical caricature, Seth Walder, has been tweeting out his hilarious takes. Walder is an ESPN NFL analyst who built a model that he claims can predict the probability of winning a game for every play to three digits of precision.

Though he maintains his sauce must remain secret, Walder claims he can determine the optimal move for any NFL play at any point in any game. His sophisticated model accounts for all aspects of the game, including teams’ strengths, the nuances of route trees, and the fluid dynamics of the air. Apparently, by looking at vast amounts of historical data and using the most cutting-edge probabilistic calculations, he can compute the probability that a team wins given their next play call. On Sundays, he loves to post graphics from his model like this:

What does this all mean? At the end of the first quarter, the Chargers had the ball on the 13-yard line. It was fourth and three, and they chose to kick a field goal rather than attempt to get a first down in hopes of continuing the drive for a touchdown. Walder’s model said the probability of winning was 53.7% if they kicked the field goal and 55.6% if they attempted the fourth-down conversion.

Where do these precise probabilities come from? He’ll never tell. On Bluesky, a commenter appropriately named “Serious Professional, PhD,” wrote, “In my experience it’s “gotta round somewhere.” Fair enough. I’ve looked into a lot of these probability calculations before, and they always end up being hacky conventions. They are definitely not precise enough to let you accurately judge whether 55.6% or 53.7% in the first quarter accurately translates into anything about winning the game.

Walder, of course, begs to differ: “This is one of those where people say “two-possession lead” when you’re way too early to think that way. It’s about point maximization and kicking, isn’t it.”

I guess he knows best.

Now, look, I’m not going to defend the Chargers, who look to have a total mess of an offense. But it is funny that Walder gets more attention than a random anon account who yells at their screen on Sundays. His cost-benefit analysis is not objective in any way. As we discussed in class, a major part of the cost-benefit framework is transparency so all stakeholders can examine the assumptions that go into computing the ratio of costs to benefits. A secret computer program that argues for maximum aggression at all times doesn’t fit the bill. It’s just a computer program he’s thrown together that says what he wants it to say.

Moreover, I will never get over how analytics people have convinced themselves that they can narrow down the infinite complexity of “going for it” to a single number. The relative complexity of attempting a kick versus running a play is vast. Kicking a field goal is the only play in football without complexity! The snapper snaps it, the holder places the ball on the ground, the kicker kicks. Sure, the field position and weather change the conditions a bit, but compare this to the complexity of what you do when you “go for it” on fourth and three. Do you run or pass? What personnel do you bring in? What route combination do you use? What does the defense do in response? It’s a complex web of decisions that Walder can’t know. But he can tell you the right answer to three digits of precision.

And speaking of the complexity of going for it versus kicking, the Jets did the go-for-2-down-8 thing again on Sunday. This is the third time under Aaron Glenn’s short coaching tenure that the Jets have found themselves down by fourteen points in the fourth quarter. They might want to work on getting leads in the fourth quarter, but that doesn’t seem part of the team’s identity.

Aaron Glenn, who spent four years as an assistant coach under Detroit Lions madman Dan Campbell, has internalized the strategy that maximizes the analytics cost-benefit analysis: score a touchdown to get within 8 and then attempt a two-point conversion. It’s certainly more aggressive, which is why Campbell’s coaching tree loves it.

Indeed, Glenn is one of the three coaches ever to have success with this desperation move. And it almost worked for him this time! He failed the first two-point conversion, but managed to get a second one with the luck of (a) foiling Campbell’s predictable run play on fourth down on the Jets’ 45, (b) driving back 55 yards for a touchdown against the Lions’ pathetic secondary, and (c) throwing a challenge flag the NFL agreed with after the conversion had apparently failed. Of course, the Lions just went and scored another touchdown on the subsequent drive, and the Jets fumbled on their final possession. So it goes.

The Jets are now 4 and 16 under Glenn. They are 1 and 3 when going for two down 8. I suppose you could argue that they are a lot better than last year, but they’ve got a long way to go before they are a good team. But Glenn gets analytics kudos because his losing moves match the model. On the broadcast, announcer Adam Amin declared, “This is an analytically advantageous place to go for two, even if you don’t get it.” Walder of course tweeted out that Glenn had passed the down 8 test. It doesn’t matter if you win. All that matters is that you adhere to the cost-benefit analysis.

I just don’t know how you watch these games and think they are more fun when you ask your computer what the right move is on every down. There’s a market for it. Some people love turning sports into escalating wars of bureaucracy. But we should at least call those people weirdos.

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Hi there, argmin readers! Today’s post is a live blog of Class 8 of my graduate seminar “Forecasting: A Critical Retrospective.” The syllabus and list of past posts are here.

A bizarre central tenet of “rational decision-making” is that all optimal decisions can be made by computing an appropriate cost-benefit analysis. I riff on this in the introduction to The Irrational Decision, and always lead with more absurd examples when I talk about the book. Should you have a surgery? Should you force your kid to take violin lessons? Should you go for it on 4th down? According to the tenets of rational choice theory, you can answer all of these questions by forecasting a dollar value and probability of every outcome.

With these facts in hand, optimal decision making is merely a mechanical chain of sums and multiplications. This is ludicrous if you think about it for two seconds. And yet it’s become a standard social convention that utilitarian calculation is not only possible but the optimal way to live your life, run a business, or govern a nation.

In today’s class, we try to get at the roots of where this came from and how it became institutionalized. My two favorite references on the history are Theodore Porter’s Trust in Numbers and Elizabeth Popp Berman’s Thinking Like an Economist, both of which trace the history in the United States.

Porter starts before the war, looking at how cost-benefit analyses were formalized to justify water projects by the Army Corps of Engineers. He has a nice short article summarizing the book’s in-depth study. Water projects were crucial for preventing flood damage, routing water to farms, and making waterways more navigable. However, they were also classic pork-barrel projects, where elected officials would funnel money back to their districts. The Corps looked for means to “remove the politics” and demonstrate that each project was worth doing. They settled on cost-benefit analysis, establishing a rigorous system to enumerate all of the potential upsides and itemize all of the potential costs.

These calculations were eventually mandated in the 1936 Flood Control Act:

“...the Federal Government should improve or participate in the improvement of navigable waters or their tributaries, including watersheds thereof, for flood-control purposes if the benefits to whomsoever they may accrue are in excess of the estimated costs, and if the lives and social security of people are otherwise adversely affected.” (italics mine)

Cost-benefit analyses would leave them with a simple, clean, unitary number — the ratio between these costs and benefits — that they could present for project approval. All of the complexity could be reduced to two digits. These digits sufficed to make governance decisions. Significant expertise was needed to ensure these calculations held up to adversarial scrutiny. As Porter writes:

“Objectivity, then, meant above all the standardization of quantitative methods and the training up of people capable of performing them. Every failure of clarity, every gap in the reasoning, every loophole that left space for the quantifier to alter the results in a preferred direction, was a potential weakness, which opponents of the agency were certain to exploit, often in hearings before judges and administrators who would probably be ignorant of the fine points of economic quantification.”

Interestingly, no economists were consulted in constructing the estimates. The engineers prided themselves on their ruthless objectivity and ability to decouple their preferences from the cold hard facts. Moreover, the public preferred cost-benefit analyses to opaque expert judgment. Standard, transparent processes feel like they rule out arbitrariness and capriciousness of bureaucrats. Porter casts cost-benefit analysis as “a quantitative decision technology, practiced mainly in public bureaucracies, often in a highly politically-charged context.”

Popp Berman details how this technology spread through the government, with the establishment of various executive-branch offices staffed by experts to oversee complex problems like healthcare and education. It became institutionalized in policy schools, founded in the 1970s to provide graduates to staff said agencies.

Fast forward to the present, and we just take these cost-benefit analyses for granted. They give an institutionalized illusion of objectivity, but of course all of the calculations are subject to institutionalized norms of expert judgment. These norms tell you where you can commit rounding errors, ignore missing data, or disregard the unenumerable. But these are just institutional norms, and they don’t really hold up to scrutiny. As Larry Lohman details, the “objective” methods of institutionalized cost-benefit analysis are riddled with value-laden assumptions, and objectivity rests on absurd ideas of commensurability and the ability to price all preferences.

Moreover, Charles Manski describes the incredible uncertainty inherent to cost-benefit calculations.1 Manski notes that experts all know these uncertainties are present but choose not to report them for political reasons. You’ll often find cost-benefit analyses reported to three or four digits of precision, creating a further illusion of precision. Manski has a long list of critiques:2

• Conventional certitude: A prediction that is generally accepted as true but is not necessarily true.

• Dueling certitudes: Contradictory predictions made with alternative assumptions.

• Conflating science and advocacy: Specifying assumptions to generate a predetermined conclusion.

• Wishful extrapolation: Using untenable assumptions to extrapolate.

• Illogical certitude: Drawing an unfounded conclusion based on logical errors.

• Media overreach: Premature or exaggerated public reporting of policy analysis.

Together, these conventions conspire to communicate certainty where there is none. They justify decisions as rational by sweeping all of the uncertainty under the rug.

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Hi there, argmin readers! As the fall semester picks up, posting volume will, too. So I’m going to commit to writing short descriptive headers to help you sort through the different threads.

Many readers have asked me to write about AI companies’ conquest of mathematics. Today’s post is a first, but by no means final, attempt at grappling with our new mathematical condition.

Early in my career, I was fortunate to get caught up in a fascinating research frenzy at the intersection of pure and applied math, the compressed sensing gold rush. Compressed sensing asked whether signals could be compressed at the time of measurement. Rather than sampling an image with a high-resolution camera and then compressing it to a JPEG, could we collect a number of samples equal to the number of bytes in the JPEG? Compressed sensing rested on deep mathematics from geometric functional analysis, convex geometry, and probability theory. It yielded multiple engineering artifacts, from faster MRI capture times to better systems for content recommendation.

Though we can see the influence of the field across many applied domains, the math of compressed sensing was never decidedly prescriptive. The theorems always assumed things about reality that couldn’t be verified or required measurement systems that were too costly or impractical. Yet the math of compressed sensing helped us focus on a shared narrative of design principles. It helped us design new algorithms. It helped us construct new measurement schemes that were robust to noise. It helped us map out which other system structures were amenable to compressive techniques. Pure math gave us a frame to see what was possible.

While this mathematical formalism was unreasonably effective, it came with a decidedly unhealthy downside. Shahar Mendelson best described this general problem of applied pure mathematics in a talk he gave at COLT 2014. Applied mathematicians often need to build a giant scaffolding of mathematical modeling to solve a problem. This scaffolding creates new mathematical puzzles that aren’t directly connected to the original problem of interest, but that entice problem solvers. You’ll then see dozens of follow-up papers solving the puzzles but forgetting the problem we cared about in the first place.

This is open problem culture, and it’s corrosive. It leads to trophy hunting, where people race to scoop each other, consult expert friends for secret insights, or steamroll each other with ever more complicated math.

This fetishization of puzzle-solving as genius has long been a destructive tendency in mathematics more broadly. It’s easy to get caught up in the thrill of it. Mathematics is arguably the most meritocratic academic discipline. There are set problems, and the people who solve them are the smart ones. Everyone forgets that the only reason problems confer status is that (a) they are currently unsolved and (b) enough mathematicians have decided these are worth solving. That (b) part is not meritocratic.

This is why many are confused and angry at the practicing mathematicians who try to explain that the discipline of mathematics is about understanding, not proving stuff. To many observers, even those who strive to become mathematicians, math seems set up as a competition from the get-go. It’s rote testing all the way up through college. Ace the SAT as a 7-year-old. Win the IMO gold as a 14-year-old. Max the Putnam Exam as a 19-year-old.

Your reward is the permission to work on whatever puzzles you want, without questions, for the rest of your life. There is no requirement for the winners to explain anything. Maybe they have to teach calculus, but they don’t have to do a good job at it.

From the outside, you can see why people think mathematics is just about winning those competitions and proving what is true. Math doesn’t send many outward signals that “understanding” is a core part of the pursuit. Most people see math as a quiz show culture. Math culture is ruthlessly competitive, and it makes a lot of people feel stupid.

The actions of many notable mathematicians have only lent credibility to their critics. Wars over credit and who gets there first have now ruined two of Clay’s Millennium Problems. This will have to change in light of recent events with AI companies solving math problems few thought they’d be able to. When computers do something we think they wouldn’t, the reaction should not be writing insanely long posts about how Eliezer Yudkowsky was right and the machines are going to kill everyone. Instead, we have to adjust our reference narrative about what we thought was true.

Indeed, I didn’t learn anything about fluid dynamics from OpenAI’s proposed solution to the Clay Millennium Prize Navier-Stokes problem. This problem is exactly the sort of puzzle artifact that I lamented above. The resolution of the Navier-Stokes problem itself tells us nothing about the dynamics of fluids that the equations attempt to model.

That said, I’ve learned a lot from the supposed resolution. I learned that the jump from rote IMO solving to the Millennium Prizes was much shorter than I expected. If you build an algorithm that’s good at solving IMO problems, and you present it with the right ingredients and computational resources, you can solve hard math problems too. That is, a lot of mathematics is training people to benchmaxx. We have already created a battery of tests, carefully tuned with the best psychometrics to find mathematical genius. Training computers to maximize those benchmarks ends up solving the benchmarks. What are millennium problems other than humanity’s final math exam?

This unfortunately makes a lot of sense with the benefit of hindsight!

If this is the lesson, there’s a funny takeaway. While it feels like you need to be an IMO prodigy to set foot in the mathematical arena, being a great IMO solver doesn’t mean you’ll become a great mathematician. For that, you need to bring other talents to bear. Despite the efforts of many smart and caring people, those talents remain ineffable. They certainly aren’t benchmarkable.

In an age of the decidedly anti-intellectual culture of artificial intelligence, mathematicians, both pure and applied, need to keep working to articulate what on earth those talents are. The statements so far, describing how mathematical programs are more than the truth values of their associated theorems, are a good start even if they are not met with universal acclaim. More need to chime in with stories about how mathematics, even the very pure variety, is valuable for scientists, engineers, and everyone else.

I can describe my own experience. Though I’m much less concerned with proving theorems than I was earlier in my career, I still consider myself an applied pure mathematician. Applied mathematics is a formal language that bridges two unbridgeable worlds. Mathematics is a deductive practice that combines axioms via a set of well-specified rules to generate lemmas, theorems, and corollaries. Empirical science and engineering are inductive. We confirm theories when they make correct predictions, willfully committing the logical fallacy of affirming the consequent. This does not make science wrong. It just means, as David Hume told us three hundred years ago, that mathematics can’t justify science.1

Applied mathematics is thus a logical language for describing inductive processes. It’s, um, unreasonably effective at this task. As captured above in my discussion of compressed sensing, it can never perfectly specify what you should do in practice. Instead, it acts as a form of linguistic technical drawing, allowing communities of scientists to build complex theories and engineers to build complex systems. Pure mathematics gives applied mathematicians new pens and brushes for those drawings.

This is why I like (and have been using throughout) Jordan Ellenberg’s term applied pure mathematics. Applied mathematics often just means the mathematics of partial differential equations. Applied pure mathematics is any application of any mathematics to anything outside of the closed world of mathematics itself. You never know which weird corner of the vast libraries of “apparently useless” mathematics will help you make sense of reality.

Let me give an example of unexpected brushwork from my time in the compressed sensing gold rush. Did I need to learn p-adic analysis as an undergrad? Maybe not, but it fixed a set of regularities and patterns in my head. I remembered Bochner’s theorem on locally compact abelian groups when Ali Rahimi and I were trying to make sense of our code generating random features. This turned into a very cool paper with a lot of practical impact. The web of facts I had gathered sitting through weird courses and reading esoteric math books shaped how I saw this applied machine learning problem. AI could likely make that connection today, but my personal education is still needed to create the prompt.

In the first lecture of my first college math course, the legendary Chicago Professor Paul Sally (IYKYK) barked that he wasn’t there to teach us facts, but to fix our brains. Sally dedicated his career to mathematics education, passionately broadening the conception of who could be a mathematician. Math wasn’t a competition for Sally. It was a way of seeing. It still can be, even if our computers now outcompete us.

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Hi there, argmin readers! As the fall semester picks up, posting volume will, too. So I’m going to commit to writing short descriptive headers to help you sort through the different threads. Today’s post is a live blog of Class 7 of my graduate seminar “Forecasting: A Critical Retrospective.” The syllabus and list of past posts is here.

In Kathryn Schulz’s New Yorker article, “The Really Big One,” she often cites figures about the chances of earthquakes.

“[T]he odds of the big Cascadia earthquake happening in the next fifty years are roughly one in three. The odds of the very big one are roughly one in ten.”

She described how these numbers arose by counting historical events and turning them into probabilities of the future. In the first week of class, we discussed this alchemy for clear discrete events. Coin flips, free throws, or elections have known times at which they occur. Only their outcome is uncertain. When we try to predict time, we need a new protocol: survival analysis.

Survival analysis is something I learned (and I think most people learn) in medical statistics. The name kind of gives it away: who do you think is surviving here other than patients in medical studies? In medicine, survival analysis captures the proportion of individuals still alive after a potentially life-extending treatment. Or, just as commonly, we flip this around and ask what proportion of subjects have not experienced a bad event yet.

In a randomized clinical trial, all patients start their timers at the same time—when they are randomized. The trialists gather the times from randomization until the bad events, and then estimate a probability distribution on the time until an event occurs. This distribution is over times, and is specified by a curve that models the chance the time to a bad event is greater than T. For example, this could be a distribution of how long it takes for cancer to progress under some new treatment. Or it could be how long until someone contracts an infection in a vaccine study. A survival curve lets you make probabilistic forecasts. For every time, you can look at the estimated proportion of individuals who have not yet experienced a bad event and call that the prognosis. “90% of patients experience no bad outcomes in the year following treatment.”

Here’s the most famous survival curve of all time. Who remembers this one?

These curves are estimated using a nonparametric method called the Kaplan-Meier estimator. The Kaplan-Meier curves give a rough shape of the survival distributions and let clinicians compare the relative effectiveness of treatments. When the treatment and control curves are far apart, it suggests something meaningful differs between the treatment and control conditions.

We can apply the same survival analysis ideas to other time-to-event forecasts. Let’s caricature how we might do it for earthquakes. For a single fault, you can imagine a major earthquake as a “reset” of the tension in the earth. Each earthquake gives you a time to start counting until the next one. If we assume every earthquake follows identical geodynamics, we can treat each earthquake like a patient in a trial, now estimating a survival curve for the time to the next earthquake. This is a crude model, as it assumes a total reset of conditions, but it’s a starting point.

Once we have this model, our historical record gives us a path to estimate the survival curve and forecast the probability of an earthquake in the next T years. Although we could build a Kaplan-Meier curve here, we could also pose an explicit model of how the probability changes over time and fit the parameters.

Any probability distribution over nonnegative numbers can serve as a model for the time to event and thus be turned into a survival curve. A common distribution in earthquakes is the exponential distribution. That is, the model is that the probability that a new major earthquake happens within T years after the first one is:

The nice thing about the exponential distribution is that it only has one parameter to estimate from data, and the maximum likelihood estimate is super simple. It’s

This formula gives us a straightforward program. Look at the historical record and compute the average waiting time between events, W. If you want probability forecasts over time windows, treat this average time as the inverse of the parameter of the exponential distribution. In this model, the probability that there will be a new event in T years is

This model is too simplistic, but it’s the first back-of-the-envelope calculation people do, and it’s where all the figures in Schulz’s New Yorker article come from.

This exponential survival model is the same as modeling earthquakes as a Poisson process. You can get fancy and make your model more sophisticated to capture more physical reality, specializing parameters to the particulars of each fault. You can model the survival function with some other distribution, be it log-normal, Weibull, or whatever. However, every modeling assumption you make adds more parameters to fit from data, and earthquakes don’t occur frequently enough to fit that many parameters to reasonable precision. If you have only forty events, you should probably estimate only one parameter.

Whatever modeling you do, survival analysis gives us another apparatus for turning counts into chances. How precise you think those chances are now rests on a whole lot of untestable modeling assumptions. What is the chance those assumptions are wrong?

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Hi there, argmin readers! As the fall semester picks up, posting volume will, too. So I’m going to commit to writing short descriptive headers to help you sort through the different threads.

Today’s post is by Jessica Dai, writing her second post on the microconference on “public feedback for AI and beyond” that she ran at UC Berkeley in August. -Ben

Today, I’ll continue blogging readouts for the AI & public feedback workshop. As a reminder, here’s some of my motivating logic:

Proposition 1. “The public” has interesting and important things to say about their experiences with AI, but are not typically listened to by decision makers.

Proposition 2. “Evaluations” — and aggregated information, more broadly — are useful, in the sense that they can influence consequential decisions.

Corollary. AI evaluations from public feedback can be a meaningful way to “do something” about the emergent misalignment between those who control AI development and literally everyone else.

In the first post about the workshop, I wrote about who, or what, “the public” refers to. Today, I’ll continue with “Proposition 1,” and try to reason through some of the challenges in the process of actually providing feedback.

Easing the burdens of “participation.”

What does a participant experience in the process of sharing information? As an economist might say, engagement is ‘costly’ — this is why, for instance, human subjects studies typically compensate participants, and why the “representativeness” of the people who self-select to participate in light of these costs remains a central challenge (I discussed some of these issues in the prior post).

But costs can manifest concretely in ways that are difficult to quantify by economic measures. Moreover, they are not only about the initial decision to participate; the process of participation itself entails challenges that can affect the outcomes of data collection. For example, Samantha Dalal, the researcher with WAO, emphasized the importance of understanding the barriers to participation that might be specific to the relevant “slice of the public.” If data will be collected via a mobile app, it should be available on a variety of platforms (including older versions of Android and iOS), and small enough to be feasibly downloaded to a phone with limited storage or on limited cellular data; online forms should be readable on mobile browsers. While these factors may seem like basic design fundamentals, they are also a reminder of the friction inherent to collecting “real” data.

Some of this friction also involves active support from facilitators that shapes the feedback itself. Some of the preliminary findings in Humphrey Obuobi’s presentation about BLOOM’s work in central Oregon were results from a Polis-like platform, where participants could provide statements of their own positions on various topics as well as engage with previously-written statements (for example, by indicating support or disagreement). Some workshop attendees noticed that these statements varied widely not just in content, but style, with some statements being noticeably longer, more detailed, and having more complex sentence structure. Humphrey explained that BLOOM uses a mix of participant-generated and facilitator-written statements in the deliberation process; the latter can synthesize existing participant-generated positions, while also help support participants to develop finer-grained perspectives.

Both of these are examples of ways that facilitators can be actively involved in the process of collecting feedback, rather than passively waiting for data to arrive; they also suggest that this involvement can ultimately result in higher-quality feedback. Another lens for thinking about these examples is legibility. If data collection platforms are poorly designed, then there will be members of the public who are “illegible” to facilitators; meanwhile, the facilitator-written statements are directly increasing the “legibility” of participants’ original statements.

Pursuing and enabling legibility in this way feels important; why? Ben’s talk provides one conceptual answer. He spoke about the quantification trap, wherein the demand for legibility is the first in a series of dominoes that ultimately requires power to be enacted only through “objective” numbers, and conversely, endows numbers (“objective,” or otherwise) with power. I’ll discuss the latter part of this statement in a later post, but I want to highlight one of Ben’s arguments (really, Graeber’s) that his post glosses over: One vector through which people experience “structural violence” is that they must work to make themselves legible to the decision makers who hold power over their lives. Any illegibility, or irregularity, excludes them from bureaucratic accounting; in Graeber’s account, this can be dangerous and, in the worst case, subject them to material harm.1

When viewed from the perspective of legibility, therefore, the various ways in which facilitators can make participants’ lives easier is also a way to prevent their exclusion from the evaluation, and whatever future conversation this evaluation enables. Some people might find it otherwise difficult to make themselves or their feedback legible, and while their resulting exclusion might not result in anything as dramatic as material danger, it still feels worthwhile for facilitators to ease whatever burdens participants face to make themselves heard.

The costs of legibility.

It is not lost on me that there are also costs to legibility. For instance, many of the projects that involve analyzing transcripts can be fairly invasive from a privacy perspective, even when transcripts are donated voluntarily, and analysis does not rise to the level of privacy violations. Similarly, any “monitoring” approach, whether it’s of product usage or of social media (as in my r/ChatGPT paper), also essentially amounts to surveillance that subjects users to a level of scrutiny they may not feel entirely comfortable with. One of the other recent California bills that Deb Raji discussed was SB243, which requires chatbot providers to track and disclose the number of conversations that mention suicide or self-harm; while requirements for such disclosures seem important for accountability and transparency, there are obvious privacy tradeoffs as well.

Perceived discomfort seems to matter. Evi Micha, from USC, has done a lot of theoretical and algorithmic work on ensuring representativeness in citizens’ assemblies (e.g., demographic, regional, etc.). Representativeness might reasonably be thought of as a necessary precondition for such assemblies to produce high-quality discussions that can be effective proxies for viewpoints of the population as a whole. In her talk, she shared findings from recent work with a different methodological perspective: how do participants actually perceive “representativeness” in assembly selection? Perhaps unsurprisingly, people generally prioritized representation in the sense of political or issue-based agreement; they would be happiest to be represented by someone who shared their views on the topics to be discussed.

What was more surprising was the degree to which people seemed to hate the idea of representativeness measured via demographic attributes. Evi shared some of the free-text commentary from study participants, and I can’t over-emphasize how strongly negative this feedback was. Participants seemed to take offense at the very idea that demographics might have any correlation, and therefore relevance, to their views on substantive issues. While we know that demographics and political views often do actually correlate on the population level, it seems like it’s worth considering how it feels to an individual for their worthiness as an assembly participant to be reduced to immutable demographic characteristics.

There’s of course a bit of a chicken-and-egg problem, in the sense that it would be difficult for any facilitator to select assemblies that were fairly representative of issue-level perspectives before even knowing what those perspectives might be or how they might be distributed across the population. It’s therefore understandable that demographics, which are easily “legible” a priori, become the fallback mechanism for ensuring “representativeness,” but this cheap legibility might be exactly what participants are chafing against.

The necessity of legibility.

In some cases, it might be necessary to explicitly impose the burden of legibility on participants, especially when the goal is to shift power to them. Ira Globus-Harris spoke about their work designing a “bias bounties” mechanism for auditing a deployed machine learning model. Specifically, the mechanism allows any population subgroup that perceives the deployed model to be inaccurate on them to submit a “bounty”; this brings the model developers’ attention to performance on that particular subgroup, allowing developers to iteratively improve the model in the future.

This framework is compelling, because it effectively identifies the power in the public as due to knowledge about their own experiences (i.e., groups of people can determine when the model is inaccurate on them specifically), and leverages that knowledge while also recognizing that only model developers have the power to actually change the model itself. The catch is that, for any given subgroup, model developers can only improve the model for that subgroup if it is statistically possible to do so. (One major takeaway from the fair machine learning research of the late 2010s is that what often appears as “bias” is often actually due to “variance” — it can be inherently harder to predict Y from X in some subgroups — so for a fixed measure of performance there may be subgroups for which that measure can never improve, no matter how complex the underlying model.)

Ira’s mechanism therefore requires that a submitted “bounty” for a given subgroup includes not just a statement that the model performs poorly on that subgroup, but also evidence that it is even possible to do better on that subgroup. This makes sense, because no model developer, no matter how benign, can do better than what is statistically achievable; on the flip side, as long as improvement is possible, “bounties” of this form allow the model developer a straightforward algorithmic approach to incorporate the reported information to implement the improvement. On the other hand, this also asks a lot of potential “bounty hunters”, including, perhaps, collecting their own data and training their own model — a requirement that might well be practically infeasible.

In this case, the mechanism specifies exactly what it means to be legible, without explicitly providing a pathway for participants to meet those criteria. Even so, I want to emphasize that the specification itself is, already, an invitation to the public. Since the goal is to change the deployed model, participants must share feedback in a way that can be legible to the model developer. The specification of what counts as “legible” is a starting point for helping participants to be seen the way they want to be seen — and ultimately, for making it clear that it is their voices we want to hear in the first place.

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