Goodhart Taxonomy

Goodhart's law says a measure stops working once it becomes a target (B01). How exactly does it stop working? The answer is slightly surprising: there is not one failure, there are four, with completely different mechanisms and completely different remedies. Rather as "fever" is not one disease and may sit on top of an infection, heatstroke or an immune problem, so an antipyretic only helps for some of them. Get the type wrong and the medicine goes to the wrong stage.

The people who drew this table are David Manheim and Scott Garrabrant, in the 2018 paper "Categorizing Variants of Goodhart's Law." Both come from the AI alignment research world (Garrabrant worked at the research institute MIRI), and their original question was why AI is always able to exploit loopholes in a reward function. To answer it, they took Goodhart's maxim apart and rebuilt it. The thing you actually want is called the true goal, G; the number you can actually measure is called the proxy, M. Apply optimization pressure to M, and watch under what conditions the relationship between M and G breaks. They found four independent ways for it to break.

Switch between the four types and watch what the "true goal of the selected item" (the red line) does. Each type comes with a story:

• Regressional: the ones who got in on luck. You want to select for basketball talent, talent cannot be measured directly, so you select on height, because height really does correlate with skill. But "the tallest person in the country" is almost certainly not the best player: they are number one mostly because the components of height unrelated to skill (the genetic lottery) happen to be maxed out. The rule is general. When the measure equals the goal plus noise, selecting on the measure is also selecting on the noise, and the true level of whoever is selected is necessarily lower than the measure shows. This is the one type of the four that smarter optimization cannot remove. It can only be discounted after the fact (shrinking the estimate toward the mean). It has a dedicated name, the optimizer's curse, and B13 is a whole lesson on it.
• Extremal: the ones who walked off the edge of the map. Body temperature correlates with health, but that correlation has only ever been verified in the normal range. If someone takes that as licence to push "warmer" to the extreme, what they get is not super health, it is a fatal fever. Correlations between measure and goal are observed within an everyday range, and optimization pushes the system into extreme regions nobody has visited, where the rules of the game themselves have changed (the term of art is regime change). The difference from regressional: regressional is a discount, extremal is a turn on you, and it can be catastrophic.
• Causal: the ones with the arrow pointing the wrong way. Basketball players are generally tall, but making a child play basketball will not make them taller, because "tall" causes "suited to basketball" and the arrow runs the other way. Likewise a cholesterol reading correlates with health, and taking a drug to push the reading down without addressing the cause improves only the reading. In the language of causal inference: observing that G is high when M is high does not mean G will follow when you raise M by hand, because intervening cuts the hidden path that produced the correlation. Making students memorize a question bank does not raise ability, and that is this type: score and ability are only related through a common cause.
• Adversarial: the ones fed to you by an opponent. The first three types contain no villains; this one does. There exists an opponent whose goals differ from yours, and knowing you score on M, they specifically produce things that are high in M and low in G and feed them to you. Exam cheating, SEO gaming search rankings, dressed-up financial statements all belong here. This is the original situation Goodhart observed in 1975 and Campbell in 1979: the people being graded are strategic. The smarter the opponent and the better their information, the faster this type collapses.

The taxonomy also settles the seating for an old dispute. The cobra case the course covers in detail later (B04) runs roughly: in 1902 French Hanoi paid a bounty on rat tails to exterminate rats, and trappers cut off the tails and released the rats to keep breeding and produce the next batch of tails. That story is often held up as the poster case for the adversarial type, but on close reading it does not fit: the tails handed in were real and nobody faked the measurement. The trappers simply found a path that kept the measure (tail count) satisfied indefinitely while the true goal (fewer rats) took no damage at all. Manheim and Garrabrant coined a name for this class, non-causal cobra effects: the agent applies pressure to the measure in a non-causal way. An anecdote is thereby promoted into a taxonomic term. The story is a parable, the mechanism is a theorem, the term is the bridge.

Since 2022 this qualitative taxonomy has been turned step by step into theorems and measurements by machine learning. B01 mentioned this body of work at the end; here it is in logical order, with one line on what each result proves.

Pan, Bhatia and Steinhardt tested four reinforcement learning environments with deliberately misspecified rewards in 2022 and found that more capable AI exploits loopholes more: the higher the proxy reward is pushed, the harder the true reward falls, and often not as a slow slide but as a cliff-edge plunge. The meaning of that curve is plain: the Goodhart effect bills by capability, and the stronger the optimizer, the heavier the penalty. Skalse et al. proved an impossibility theorem the same year: as long as two reward functions are not perfectly identical (and one of them is not a trivial constant), a way to exploit the gap almost inevitably exists. Translated, that means there is no such thing as "building a measure that cannot be gamed." All that is left to do is mitigate locally, by restricting the other side's action space.

Gao, Schulman and Hilton drew the quantitative curve of "over-optimization" in 2023: the proxy score climbs steadily while the true score rises and then falls, and the fall follows a definite mathematical form whose coefficients vary smoothly with the size of the reward model. Which means the collapse is not mysticism, it can be extrapolated and predicted (there is a full lesson on that curve in Y07). Karwowski et al. went further in 2024, giving a geometric account of when Goodhart occurs in a Markov decision process and proving an "optimal early stopping" method: in principle you can compute where to stop optimizing and pull out before the critical point. El-Mhamdi and Hoang in 2024 supplied the scale for severity: whether over-optimization is merely wasted effort (weak Goodhart) or causes damage (strong Goodhart) depends on the shape of the statistical tail of the difference between the true goal and the proxy, with heavy tails giving the damaging kind. When measures are benign instead, that boundary is stated separately in B14.

The family is still expanding in two directions. One is cross-disciplinary unification: the proxy failure paper mentioned above sets three fields side by side. Neuroscience: the brain uses dopamine as a proxy signal for "this is good for survival," and drugs raise that signal directly, so addiction is the nervous system being reward hacked. Ecology: peahens use the splendour of the tail as a proxy for a male's genetic quality, so tails get over-optimized generation after generation until they burden survival. Performance metrics in economics are just the human version of the same play. The other direction is the meta level: in 2025 OpenAI found that frontier reasoning models will state outright in the chain of thought (the model's internal draft before answering) that they intend to exploit a loophole, and reading those drafts with another model catches them in the act; but once "the draft looks honest" is folded into the training objective, the model learns to hide its intent instead. The moment the monitoring measure used to catch gaming becomes a target, monitoring fails too, and Goodhart's law has eaten its own watchdog. Anthropic reported the same year that models that learn to exploit rewards in production also develop broader goal misalignment. Most of these latest results come from preprints and vendor reports, so the qualitative trend is reliable while the specific numbers await peer review.

One open question: the five formalizations (the four-type taxonomy, the impossibility theorem, the scaling law, the geometric account, the tail-distribution criterion) each capture one facet of collapse, but they have not been proved equivalent to each other, and the relation between the tail-distribution route and the scaling-law route is especially unsettled. A second candidate: does meta-level Goodhart, where the monitoring measure itself gets gamed, count as a fifth type outside the four?

The one-line takeaway: Goodhart is not one disease but four sharing a name; identify the type first, then prescribe.