Seven units, with the primary sources, the model to master, and the experiment to reproduce in each
The problem of knowing whether unattended work was any good is old, rigorous, and scattered across six fields that do not cite each other. This curriculum assembles it. Unit I takes the measurement of unobservable quantities from psychometrics, where it has been formalised for a century. Unit II takes the design of experiments, including the sequential designs a budgeted run needs. Units III and IV take the economics of delegation: first the contract offered to one agent, then the structure that divides work among many. Unit V takes proxy failure, made quantitative. Unit VI takes comparative judgment, which is how a judge becomes an instrument rather than an opinion. Unit VII takes scalable oversight, and asks what remains possible when the supervised party is more capable than the supervisor.
Each unit names a small number of primary sources, one mathematical model to be understood well enough to derive, and one foundational experiment to be reproduced from scratch. Six of the seven replications need no model calls and no budget, only an afternoon and an honest plot.
Read in order. The dependencies are real. Unit V's formalisation of proxy failure is unreadable without Unit I's distinction between a construct and its indicators, and Unit VII's oversight results are anecdotes without Unit VI's machinery for turning verdicts into a scale with error bars.
Each unit is done when its replication runs and its result is written up, not when its reading is finished. The replication is the exam. Where a replication touches this repository's own data, it is stated, and those can be run today at zero model cost because the data already exists.
Runs conducted during the curriculum follow the house standard, which is short and was derived from three prior runs here that each failed the same way.
There is no department, no canonical textbook, and no agreed name. There are instead six mature literatures whose intersection nobody has occupied. That is the opportunity and also the hazard, since nothing here will tell you that you have assembled the pieces correctly, and the characteristic failure of an autodidact in a pre-paradigmatic field is to reinvent, badly, something settled in 1955. The reading lists below lean old for that reason.
If quality cannot be observed directly, on what grounds may a number be said to measure it?
This is the oldest rigorous part of the field and the part current practice most completely ignores. Psychometrics has spent a hundred years on one problem: inferring an unobservable quantity from fallible indicators, and establishing when you are entitled to. Spearman began it by noticing that correlations among unrelated school subjects had a structure implying a common cause nobody could measure. Everything since is the discipline of not fooling yourself about that inference.
Construct validity carries the unit. A measure is not validated by being precise, reproducible, or agreed upon, but by an accumulating argument that it stands in the relations to other things that the construct would stand in. Campbell and Fiske sharpen this into a two-sided test: a measure must converge with other measures of the same construct and diverge from measures of different ones. Most published evaluations of agent output test neither.
Classical test theory, and reliability as a variance ratio. An observed score decomposes into a true score and independent error:
Reliability is the fraction of observed variance that is signal:
Master three consequences. Attenuation: the observed correlation between two unreliable measures is bounded by √(ρXX′ρYY′), so a weak judge-to-human correlation may indicate a noisy judge rather than a wrong one, and you cannot tell which without knowing both reliabilities. Spearman–Brown: lengthening a test raises reliability predictably, which prices the question of how many rubric items you need. And a measure with a ceiling has σ²T crushed toward zero among the cases near the top, so its reliability collapses exactly where you needed it, among your best subjects.
A rater study on our own data, and the ceiling it will find. Draw a sample of artifacts from the loop and the two bake-offs. Write a five-item rubric. Have three raters score every artifact independently, at least one of them human, at least one of them you. Then compute, from scratch rather than from a library: inter-rater agreement (Krippendorff's α, which tolerates a ragged panel), Cronbach's α across items, and each item's item-total correlation.
The findings to look for are unflattering and specific. An item whose item-total correlation is near zero measures something else and should be cut. If α across items is very high, the five items are one item. And the three existing instruments should be shown formally to have almost no discriminating power: the loop's probe sat at its maximum in 59 of 89 turns, and across the two bake-offs 23 runs of 23 passed every automated check. Demonstrating that with a reliability coefficient rather than an eyebrow is the unit's exam.
What must be arranged in advance for a comparison to license a conclusion, and how do you spend a fixed budget across it?
Fisher's insight was that randomisation is not a hygiene measure but the thing that creates the reference distribution against which a result is judged. Without it you have a story; with it you have a calculable probability. The lady tasting tea is the whole argument in one page, and it remains the cleanest introduction to inference ever written.
The second half of the unit is what a budgeted run needs. A run that checks its results as it goes and stops when they look good has an error rate far worse than it believes. Wald solved this in 1945: the sequential probability ratio test permits early stopping while keeping an honest error rate, provided the stopping rule was fixed in advance. The allocation question, given a budget, is the bandit literature , of which the relevant chapter here is best-arm identification rather than regret minimisation .
Randomisation inference, then power. The permutation test needs no distributional assumption. Under the null that treatment does nothing, the observed assignment is one of C(n, k) equally likely assignments, and the p-value is the fraction of them giving a statistic at least as extreme. For eight cups, four of each:
Then the design question, where most studies are lost before they start. For a two-arm comparison of means at significance α and power 1−β, the sample per arm is approximately
Master this well enough to run it backwards. Given the budget you actually have, what is the smallest effect the study could detect? If that number exceeds any effect you believe in, the study is not worth running, and knowing so beforehand is the highest-return skill in the unit.
The lady tasting tea, exactly, then our own power analysis. Implement the exact null distribution by enumeration rather than simulation or a library call: all 70 assignments, the statistic on each, the p-value by counting. Confirm 1/70. Then extend it: recompute for six cups and for ten, and watch how fast the smallest achievable p-value moves. This is why the eight-cup design was chosen, and it is a design decision rather than a detail.
Then turn the machinery on the programme. Given a turn budget, and a quality measure with the reliability estimated in Unit I, what is the smallest per-turn improvement the curve could detect? Produce the number before running anything. An embarrassing answer means the unit is working.
Built. This unit's apparatus exists at the harness: sample size and minimum detectable effect, the pairing calculation, variance components, sequential boundaries, and the tea experiment by exact enumeration, under 92 known-answer checks. Applied to the bake-offs it reports a detectable effect of 2.8 standard deviations, which is the retrospective this unit was for.
What contract should a principal offer an agent whose effort cannot be seen, only inferred from a noisy outcome?
This unit and the next put project management and alignment on one continuum rather than at two ends of a ladder. Both are instances of the principal-agent problem: a principal wants outcomes, an agent chooses actions, and the principal observes a signal informative about those actions but not equal to them. Everything interesting follows from that gap .
Two results carry the unit. Holmström's informativeness principle holds that any signal carrying incremental information about effort should enter the contract, however noisy, which is a formal argument against reducing evaluation to one headline metric and in favour of the multiple imperfect signals Unit I taught you to combine. Then the result this programme has already paid for:
When an agent's effort is divided among several tasks and only some are measurable, effort flows to the measured tasks. The optimal response is frequently to weaken the incentive on the measurable task rather than to strengthen it, and where the unmeasured task matters enough, to offer no performance incentive at all.
the multitask result, Holmström & Milgrom 1991
Baker completes the picture by separating two defects a metric can have. It can be noisy, which costs the agent risk, and it can be distorted, meaning maximising it does not maximise value. These call for opposite remedies, and confusing them is the most common error in gate design. Kerr gives the same lesson without algebra and is the right thing to hand a colleague. Gibbons and Prendergast survey the field.
The linear-exponential-normal (LEN) model. The one closed-form model in this curriculum, and worth knowing by heart. An agent exerts effort e at cost ½ce²; output is observed with noise, x = e + ε with ε ∼ N(0, σ²); the contract is linear, w = α + βx; the agent has constant absolute risk aversion r. Maximising certainty equivalent gives effort e* = β/c, and the principal's optimal incentive intensity is
Read what it says. Incentive intensity should fall as the measure gets noisier, as the agent grows more risk-averse, and as effort gets costlier to vary. A noisy gate should be weighted less rather than compensated for by being weighted more, which is the opposite of what a failing loop usually does to itself.
Now extend to two tasks with efforts e₁, e₂, where only task 1 is measurable and the cost function has a positive cross-partial, so the tasks compete for the same effort. Optimal β₁ is pushed below its single-task value, and as task 2's marginal value rises, β₁ → 0. Derive that. It is the exam question, and a formal statement of why turns 36 to 50 of our own loop produced seven backend modules and no page.
Solve the LEN optimum numerically, then reproduce the multitask incentive-weakening result. Implement the single-task model, verify β* = 1/(1 + rcσ²) against a numerical optimiser, and plot β* against σ². Then build the two-task version and produce the paper's qualitative result: the surface of optimal β₁ over task 2's value and the cost cross-partial, showing the region where the optimum switches the measured incentive off entirely.
Finish by fitting the model to us. Take task 1 as passing the gates and task 2 as a stranger wanting to use the result, estimate the loop's implied β₁, and state what the model says it should have been. This is the first point in the curriculum where the theory makes a falsifiable retrodiction about our own run.
How should work be divided among many agents, who is entitled to decide what, and what determines when a problem travels upward?
Unit III fixes the contract with one agent. This unit fixes the structure among several, and it is the unit with the most direct operational payoff, because every question that arises when orchestrating a fleet was asked first about firms and answered with models that still hold.
Coase asked why firms exist rather than contracting everything through markets, and answered that using the market has costs. The same calculation decides whether to spawn a sub-agent or do the work in one context: the sub-agent buys parallelism and a clean context window, and costs a specification, a handoff, and a review. Williamson and Hart and Moore develop the boundary further, the latter on incomplete contracts, where you cannot specify everything in advance and what matters is who holds residual control over the unspecified parts.
Two papers are worth more than the rest combined for our purposes. Garicano models an organisation as a device for matching problems to knowledge: workers handle routine cases and escalate exceptions to specialists, and the optimum sets span of control and the number of layers from communication cost and the difficulty distribution. It is a theory of orchestration written before there was anything to orchestrate. Aghion and Tirole separate formal authority, the right to decide, from real authority, effective control over what gets decided, and show that an overloaded principal who retains formal authority ends up with less real authority than one who delegates. That is the abstraction-ladder problem stated as a theorem.
Dessein quantifies the companion question of when to stop specifying and start delegating: because communication loses information, delegation beats an informed principal issuing instructions once the preference gap is small enough. Galbraith supplies the framing that transfers most cleanly, treating structure as a choice matched to the volume of exceptions that must travel up it.
Garicano's knowledge hierarchy. Production requires solving problems drawn from a known distribution. A worker learns some interval of that distribution and solves the problems falling in it; problems outside it are passed up at communication cost h to a specialist who has learned rarer material. With a fraction p of problems solved at the first layer, one specialist can support a span of roughly
Derive the layer structure and the comparative statics. Falling communication cost widens spans; a harder problem distribution deepens the hierarchy; and the value of the specialist's time rises with the number of exceptions they field rather than with the total work below them.
Then read the quantities off our own setup. The worker is a sub-agent, the specialist is the orchestrator, and h is the real cost of a handoff: writing the brief, reading the diff, and repairing a misunderstanding. The model says what your span should be, and it also says the thing people find counter-intuitive, which is that lowering h by writing better briefs raises the number of agents you can usefully run more than making the agents better does.
Fit the knowledge hierarchy to a real orchestration run, then test its prediction. Take the loop's ledger, which records 656 beads and 195 dependency edges, and the two bake-offs. Measure the escalation rate, meaning the fraction of work items that required the orchestrator or a human, and estimate h from the time and tokens spent on briefs, reviews and repairs. Compute the implied optimal span and compare it to the span actually run.
Then the test, which is the part that makes this an experiment rather than an exercise: the model predicts that halving h should raise the usable span by more than a proportionate improvement in first-layer solve rate p. Both are manipulable. Better briefs lower h; a stronger model raises p. Run the two-by-two under the house standard and see whether the ordering holds.
The cheaper prior replication, done first: Leavitt with agents in the seats. Wire the same task as a chain, a wheel and a bottleneck, hold the turn count at six, and measure accuracy and time by position. WP2 is the design; it costs 180 turns for a d = 0.8 contrast and needs no new apparatus.
WP4 takes the third: if a turn only removes a defect it can see, what does a check change? A check is re-run rather than remembered, so it does not attenuate — which would end the matter, except that a check is written by a turn, and what it gets wrong it certifies as passing. The result is a stopping point rather than a target, and a choice between specifying first and building twice.
WP3 then asks the same unit's second question. A person at a handoff supplies context and correction; wiring already buys the first, so what does the second cost in turns? The answer is an exchange rate between unattended and directed turns, and over a third of the plausible parameter space it does not exist.
Exactly how, and how fast, does optimising a measure destroy its relationship to the thing it measured?
Goodhart's original remark was narrow and about monetary aggregates; Campbell stated the general version better and earlier than the slogan's history suggests, and Strathern supplied the familiar phrasing along with an ethnographer's account of what a measured institution becomes. The essential modern move is Manheim and Garrabrant's : Goodhart's law names at least four distinct mechanisms, and they have different fixes.
Internalise the regressional variant first, because it requires no adversary, no gaming and no intent, only noise and selection. If a proxy equals the true quantity plus independent noise, selecting the top scorer selects partly for quality and partly for luck, and the expected true value of the winner falls short of its measured value by an amount that grows with selection pressure. Nothing has malfunctioned and the number still misleads.
Then the quantitative anchor for the whole programme. Gao, Schulman and Hilton measure gold-standard quality as a function of how hard a proxy is optimised, and fit functional forms in which quality rises, peaks, and declines with continued optimisation. Our own question, whether turn 20 improves on turn 19, is a special case of theirs with turn count standing in for optimisation pressure. Pan, Bhatia and Steinhardt add that the transition can be abrupt rather than gradual. Skalse et al. give "unhackable" a formal definition and show how restrictive it is.
The unit carries a set of documented cases, because the mechanisms are easier to recognise in institutions than in one's own pipeline. Bevan and Hood is the best empirical study of target gaming in a real system: ambulance clocks restarted, waiting lists reclassified, patients held in corridors so the trolley clock never began. Every one of those has an analogue in an agent gate. Hood generalises the taxonomy.
Lazear is included deliberately as the control case. A switch from hourly wages to piece rates at a windscreen fitter raised output by roughly 44%, about half from existing workers working harder and about half from the change in who the scheme attracted. Incentives work. A unit that only collects failures teaches the wrong lesson, and the interesting question is what distinguished Safelite's setting, where the measure was close to the whole job, from the health-service targets, where it was not. That distinction is Baker's from Unit III.
Amodei et al. §3 stated the agenda in 2016, and Krakovna's specimen list is the cabinet to read before designing any gate.
Regressional Goodhart, as an order statistic. Let true quality be T and the proxy P = T + E with E independent noise. Select the best of n candidates by P. In the jointly normal case the winner's expected true quality is the measured score shrunk by a factor:
Units I and V are the same algebra seen from two ends, which is where the curriculum locks together. As n grows the measured maximum keeps climbing while the true value behind it flattens, so the gap between what a gate reports and what you received widens with every additional candidate screened. No malice is required.
Produce the overoptimisation curve on a synthetic, with no models involved. Draw T from a normal; form P = T + E at several noise levels; for each n in a geometric sweep, select best-of-n by P and record the winner's mean true quality. Plot true quality against log n per noise level.
You will recover the qualitative shape of the published curves, and once you let the proxy be distorted rather than merely noisy, the curve turns over and falls. Then state the result in the form that is useful: at our measured reliability, at what selection pressure does further optimisation stop buying real quality? That number is a budget policy, derived rather than guessed.
How do you convert subjective verdicts into a scale with standard errors, and establish that the judge measures the work rather than its length?
Thurstone established that people are far better at choosing between two things than at scoring one out of ten, and gave the model turning the former into the latter. Bradley and Terry supplied the form still in use, and Elo made it famous in a setting where the predictions get checked every weekend.
The modern half is a warning. Zheng et al. document position bias, verbosity bias and self-enhancement bias in model judges, and report agreement against the human-to-human ceiling rather than against an imagined perfect standard. That comparison is the correct one and is usually omitted. Dubois et al. then demonstrate the professional response to a known bias, which is to measure it and regress it out. You do not ask a biased instrument to stop being biased; you characterise the bias and correct for it, as Unit I would have told you.
Bradley–Terry, fitted by hand. Each item i has a latent strength θᵢ, and
Fit by maximum likelihood. The minorisation-maximisation update converges in a few dozen iterations and runs to about forty lines. Take standard errors from the observed information, and note the structural fact that a disconnected comparison graph has no unique fit: an item compared to nothing has no rating, so the scheduler must be told to keep the graph connected.
Then extend it as Unit V demands, by adding covariates. A Bradley–Terry model with a length term estimates strength while holding verbosity fixed, which is how you find out whether the judge was ever measuring anything else.
Fit Bradley–Terry to real verdicts, then measure your judge's position bias.
The bake-off entries are sitting there unranked, 23 of them, with a judge panel that
returned null twice. Generate pairwise comparisons over them, fit the
model, and produce a ranking with error bars. Then run the bias experiment from
: present every pair in both orders and measure
the flip rate. A judge that flips on a material fraction of swapped pairs has an effect
size for slot position that you can estimate and compare against the quality difference
you were trying to detect.
The unit passes when you can state judge agreement with human raters as a fraction of the human-to-human ceiling, and not before. If people agree with each other 75% of the time, a judge at 72% is near the measurement limit and further tuning chases noise.
What supervision remains possible when the supervised party is more capable, at the task, than the supervisor?
Here the curriculum's halves meet, and the ordinary management intuition turns out to be the technically load-bearing one. Supervision is possible because of an asymmetry: judging is easier than doing. A manager need not out-code the engineer and a referee need not out-play the players. Wherever verification is cheaper than generation, a weaker party can supervise a stronger one, and the research programme consists of finding how far that asymmetry stretches and what to do where it snaps.
Christiano et al. is the hinge, taking the comparative judgment of Unit VI and using it as a training signal, so a supervisor who cannot demonstrate the task can still shape it. Debate and amplification propose stretching the asymmetry deliberately; self-critique is the most immediately usable, since critiques demonstrably help humans find flaws they would otherwise miss.
The unit's experimental centre is Bowman et al. and the sandwiching design: place the system between a non-expert supervisor and a ground-truth expert, and measure whether the non-expert working with the system reaches the expert's answer. It converts a philosophical worry into a measurable quantity, it is the only design here that directly tests management beyond one's ken, and it runs at our scale. Burns et al. examine the case where the supervisor is definitively weaker, and Bai et al. show a working system built on the asymmetry.
The verification-generation gap, stated as a decision problem. Let a supervisor's probability of correctly ranking two outputs be a function of the quality gap between them and of the supervisor's own competence. Supervision succeeds while that probability stays above chance in the region where candidate outputs actually differ. Formalise it, then notice the two ways it fails: the gap shrinks, so candidates are near-equally good and the judge reads noise, which is Unit I's ceiling again; or the supervisor's discrimination decays faster than the quality difference grows.
No settled model with a canonical citation covers this, so treat building one as part of the unit's work rather than as background. It is also the likeliest place in the curriculum to produce something new, because the measurement-theoretic framing of Units I and VI is not standard in the oversight literature.
A sandwiching trial on a domain where you are honestly the non-expert. Choose a task in this repository where ground truth exists and you do not personally have it: a proof in the geometry pack, a claim in the crypto stack, a numerical result with a published reference. Establish the expert answer independently. Then measure three conditions: you alone, you assisted by the system, and the system alone. The quantity of interest is the fraction of the gap between you-alone and expert that the assisted condition closes.
Report it even if negative. A trial where assistance made you more confidently wrong is the most valuable result the unit can produce, and the one this curriculum exists to be able to recognise.
At the end the claim you are entitled to make is narrow and worth having: that you can state what quality means for a class of delegated work, measure it with a known reliability, detect a stated effect size with stated power, choose a span of control and an escalation policy from a model rather than a hunch, recognise the point at which further optimisation stops buying real quality, and supervise work you could not have produced yourself, with a number attached to how far that last one stretches.
Nobody is going to hand you that. The six parent literatures are mature and the intersection is empty, which is the only reason a project of this size is worth attempting from outside an institution.
Thirty-six weeks is the honest estimate at a serious part-time pace, and Units III, IV and VII will each take longer than budgeted. Units I, II and V can be compressed if the replications are done and the reading skimmed. Units III, IV and VI cannot, because their models must be derivable rather than merely recognised. If the schedule slips, cut Unit VII's proposals (debate, amplification) and keep its replication.
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