Goodhart's Law

The law is quoted as if it were one claim. It is at least four, and they fail for different reasons.

Goodhart's own version was about statistics, not people's motives. His 1975 phrasing was roughly: any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes. His example was British monetary policy. The Bank of England had noticed a stable relationship between a particular measure of the money supply and the wider economy, and started to target that measure. The relationship promptly stopped holding, partly because banks reorganised their balance sheets around the definition being targeted. Goodhart never called it a law; other people did.

Campbell's Law (Donald T. Campbell, 1979) is about corruption of the process: the more any quantitative social indicator is used for social decision-making, the more it will distort and corrupt the social processes it was intended to monitor. Campbell was writing about crime statistics and standardised testing, and he is the more useful citation for anything involving public policy.

The Lucas critique (Robert Lucas, 1976) is the formal economic sibling. Relationships estimated from past data are not structural facts; they encode the policy regime in force when the data was generated. Change the regime and the parameters change with it. Lucas won a Nobel Prize substantially for this argument.

Strathern's phrasing (1997), written about audit in British universities, is the version on every slide deck. She offered it as a compression of Goodhart, and in compressing it she broadened it: hers is a claim about measurement in institutions generally, not about econometric regularities.

Is it a law?

No, and this is where the interesting disagreement sits. Some measures survive being targeted quite well.

The distinguishing feature seems to be how tight the causal link is between the measure and the goal, and how expensive the shortcuts are. "Number of aircraft that landed without crashing" is nearly impossible to game while producing more crashes. "Revenue" is a poor proxy for company health but a resilient one, because faking it is fraud with prison attached. Metrics decay fastest where the measured party controls the measurement, the shortcuts are legal, and nobody is checking the goal directly.

David Manheim and Scott Garrabrant (2018) proposed a useful taxonomy of the ways a proxy can fail — through ordinary statistical regression, through pushing into the extreme tail where the relationship never held, through breaking the causal structure that made the proxy work, and through an adversary who exploits it deliberately. These call for different defences, which is why "just pick a better metric" is rarely the answer.

The practical responses are all imperfect and all worth knowing: use several measures that are hard to game simultaneously; keep some measures secret or sampled at random; separate the people who set targets from those who report them; audit against the goal rather than the proxy; and retire metrics on a schedule before they have finished decaying.

1975. Charles Goodhart, then chief monetary adviser at the Bank of England, presented "Problems of Monetary Management: The U.K. Experience" at a conference in Australia; it appeared in the Reserve Bank of Australia's Papers in Monetary Economics. The context matters. Under the 1971 Competition and Credit Control reforms, Britain had begun steering policy by monetary aggregates. Goodhart's point was diagnostic and specific: the historically stable relationships between those aggregates and the real economy broke down precisely because they were being used as controls. The paper is largely about British banking; the law is an aside in it.

1976. Robert Lucas published the Lucas critique, arriving at a structurally identical conclusion from macroeconomic theory rather than from central banking practice. The two results were independent.

1979. Donald Campbell published "Assessing the Impact of Planned Social Change", having circulated it as an occasional paper from 1976. His examples — police departments improving their clearance rates, schools improving their test scores — were drawn from American public administration, and Campbell was explicit that the corruption was often unconscious.

1997. Marilyn Strathern, writing on audit culture in British universities in the European Review, produced the compressed form: "When a measure becomes a target, it ceases to be a good measure." This is the sentence that travelled. It is now attributed to Goodhart on a daily basis, including by people who have read neither paper.

2010s onwards. The law was rediscovered by the machine learning community under the names reward hacking and specification gaming, and by the management literature under the heading of metric fixation. Goodhart, still publishing, has been gracious about the whole thing.

Goodhart's Law is the reason a very large amount of institutional effort is spent on activity that no one wants.

It explains a specific, recurring failure of well-intentioned reform. Someone notices a problem. They select an indicator. They attach consequences — funding, promotion, inspection, a bonus. The indicator improves. The problem does not. And because the indicator improved, the reform is judged a success and extended.

Three consequences worth stating plainly:

Measured improvement is not evidence of improvement once the measure is incentivised. This is the single most useful thing to take away. If a number moved after you started rewarding it, that number can no longer be used as evidence about the world. You need a different, unrewarded measurement to check.

Accountability systems consume the trust they run on. Campbell's version is the sharper one here. Once everyone knows the indicator is what counts, the professional judgement the indicator was supposed to summarise starts to erode — people stop asking whether the patient got better and start asking whether the box was ticked.

It bounds how far you can manage what you cannot directly see. Any large organisation, government or algorithm has to act on summaries. Goodhart's Law says those summaries have a shelf life that shortens the harder you push on them.

Reward hacking in reinforcement learning. Goodhart's Law is now a core concept in AI safety, where it appears as the gap between the reward function you wrote and the behaviour you wanted. Amodei and colleagues (2016) listed reward hacking among five concrete problems in AI safety. DeepMind researchers maintain a public catalogue of specification gaming examples running to dozens of cases: a simulated robot that learned to hover its gripper above a block because the camera angle made it look like grasping; an evolved organism that grew tall and fell over rather than learning to walk; agents that crashed the simulator because a crashed simulator scored infinitely well.

Reward models and language models. Systems trained with reinforcement learning from human feedback optimise against a learned model of human approval. That model is a proxy for approval, which is itself a proxy for quality. Push the optimisation hard enough and measured reward keeps rising while actual quality falls — a phenomenon documented under the name reward model overoptimisation, and one of the reasons such training is deliberately kept away from the maximum. Sycophancy is the everyday symptom: agreeing with the user scores well on approval and poorly on truth.

Benchmarks. Machine learning has run on shared benchmarks for thirty years, and a benchmark is a target by construction. When a benchmark becomes the way models are compared and funded, scores rise for reasons unrelated to capability: test data leaks into training sets, hyperparameters are tuned against the test split across thousands of published papers, and the benchmark's specific quirks get learned. The field's response — retiring saturated benchmarks, holding out private test sets, building contamination checks — is Goodhart mitigation whether or not it is called that.

Engagement metrics. Recommendation systems optimise watch time, clicks or sessions because those are measurable and satisfaction is not. The known consequence is a drift towards content that captures attention rather than content people are glad to have seen, and it is the largest live experiment in Goodhart's Law ever run.

Management by metric. Hospital waiting-time targets, school league tables, research assessment exercises, sales quotas and OKRs all sit squarely in the law's territory. The practical lesson from thirty years of this is not to stop measuring but to keep a firewall between measures used for learning and measures used for judgement — and to accept that once a number is attached to someone's salary, it has stopped being data about the world and started being data about the incentive.

Write $G$ for the goal you care about and $M$ for the measure you can observe. The reason anyone adopts $M$ is that in historical data,

$$\operatorname{corr}(M, G) \gg 0$$

Model the relationship as a signal plus everything else:

$$M = G + \varepsilon$$

where $\varepsilon$ collects measurement noise, gaming, and every other influence on $M$ that is not $G$.

Regressional Goodhart. Suppose you now select for high $M$ — you promote the top decile, or fund the highest-scoring proposals. Conditional on $M$ being large, you have selected on $G + \varepsilon$, so you have selected partly on $\varepsilon$. The expected goal achieved is

$$\mathbb{E}[G \mid M = m] = m - \mathbb{E}[\varepsilon \mid M = m] < m$$

and the shortfall grows with the variance of $\varepsilon$. This happens with no strategic behaviour at all. It is regression to the mean, and it is why the best-performing unit on any noisy metric almost always disappoints next year.

Extremal Goodhart. The correlation between $M$ and $G$ was estimated over the range of $M$ observed historically. Optimisation pushes $M$ far outside that range, where nothing was ever verified. A relationship that is real over a typical range can vanish or invert at the extremes — more study hours improve exam performance until sleep deprivation reverses it.

Causal Goodhart. This is the one that separates observation from control. Suppose $M$ and $G$ are correlated because a common cause $C$ drives both. Then observationally

$$P(G \mid M) \neq P(G \mid \operatorname{do}(M))$$

Reading the measure is informative; intervening on it is not. Rewarding schools for attendance raises attendance without touching whatever made attendance predictive of learning. Goodhart's original monetary case is exactly this: the aggregate was a symptom of conditions in the banking system, and targeting the symptom simply caused banks to reclassify liabilities.

Adversarial Goodhart. Add an agent whose payoff is a function of $M$ and who pays cost $c_G$ for genuine improvement and $c_\varepsilon$ for gaming. A rational agent allocates effort to whichever is cheaper per unit of $M$. Gaming dominates whenever

$$c_\varepsilon < c_G$$

which is the usual case, because gaming exploits the specification while genuine improvement has to move the world. Raising the reward attached to $M$ does not fix this — it scales both sides equally and simply increases the absolute amount of gaming.

The four failures need different remedies. Regressional Goodhart is fixed by shrinkage and by not over-reading noisy rankings. Extremal Goodhart is fixed by constraining optimisation to the range where the proxy was validated — conservative optimisation, or a KL penalty against a trusted baseline in the machine learning version. Causal Goodhart requires knowing the causal graph, not just the correlations. Adversarial Goodhart requires changing the cost structure: auditing, randomised verification, or multiple proxies that cannot all be gamed by the same manoeuvre.