Goodhart's Law

Goodhart's law is a foundational principle in business and economics theory, econometrics, organizational governance, and artificial intelligence alignment stating that when an empirical proxy metric is selected as a target for policy control or incentive reward, the statistical relationship linking that proxy to the underlying goal breaks down. Originally formulated by British monetary economist Charles Goodhart in a 1975 Bank of England paper examining the failure of quantitative monetary aggregates in United Kingdom monetary policy, the law was subsequently condensed into its popular canonical epigram by British social anthropologist Marilyn Strathern (1997): "When a measure becomes a target, it ceases to be a good measure." Across macroeconomics, contract theory, and statistical decision theory, Goodhart's law explains why high-powered incentives tied to imperfect performance indicators trigger strategic gaming, selection distortion, and structural decoupling between measured proxy metrics (M) and true social or organizational welfare (G).

Charles Goodhart's 1975 Monetary Policy Formulation

During the stagflation of the early 1970s, central banks in the United Kingdom and the United States sought to contain inflation by adopting monetarist rules that targeted specific statistical definitions of the money stock—such as narrow money (M1) or broad sterling money (M3)—which had historically exhibited stable velocity correlations with nominal gross domestic product. After the Bank of England introduced its Competition and Credit Control reforms in 1971 and began targeting M3, commercial banks innovated around the regulatory boundary (known as the "corset" or supplementary special deposits scheme) by shifting deposits and credit into untargeted near-money instruments and offshore Eurosterling accounts, causing the previously stable econometric correlation between M3 and nominal income to disintegrate.

At the Reserve Bank of Australia's Conference in Monetary Economics in July 1975 (later republished in his 1984 volume Monetary Theory and Practice), Charles Goodhart articulated the precise econometric formulation of his law:

Convergence with the Lucas Critique, Campbell's Law, and Multi-Task Principal–Agent Theory

Goodhart's 1975 insight emerged concurrently with two parallel pillars of modern social science and mechanism design:

1. The Lucas Critique (Robert E. Lucas Jr., 1976): Published one year after Goodhart's paper, the Lucas critique demonstrated that the reduced-form parameters of macroeconometric forecasting equations (such as an empirically estimated Phillips curve trade-off between inflation and unemployment) are not structural constants of nature, but rather reflect the optimal decision rules of forward-looking rational agents given a specific policy regime. When policymakers change the policy rule to exploit a historical correlation, private agents re-optimize their expectations and behavior in game theory, shifting the reduced-form parameters and invalidating the historical correlation.
2. Campbell's Law (Donald T. Campbell, 1976): Formulated independently by American psychologist and social scientist Donald T. Campbell in his evaluation of standardized educational testing and public-sector performance auditing, Campbell's law states: "The more any quantitative social indicator is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor."
3. Holmström–Milgrom Multi-Task Principal–Agent Model (1991): Bengt Holmström and Paul Milgrom provided the formal microeconomic proof of Goodhart's law within the principal-agent problem under information asymmetry and moral hazard. When an agent performs multiple tasks—some easily quantifiable (e₁, such as assembly speed or standardized test drills) and others unquantifiable (e₂, such as long-term product durability or deep conceptual reasoning)—tying high-powered piece-rate bonuses to the measurable proxy M = e₁ + ε induces the rational agent to reallocate effort away from the unmeasured dimension e₂ toward e₁, reducing overall principal value G(e₁, e₂).

In 2018, decision theorists David Manheim and Scott Garrabrant unified the statistical, causal, and game-theoretic mechanisms underlying Goodhart's law by decomposing the divergence between a maximized proxy metric M and a true objective goal G into four distinct failure modes:

1. Regressional Goodhart (Noise Exploitation)

Suppose the observable proxy metric M is an unbiased noisy measurement of the true latent goal G, such that M = G + ε, where G ∼ N(μ_G, σ_G²) and the measurement error ε ∼ N(0, σ_ε²) is independent of G. For any randomly drawn unit in the population, E[G | M] is positively correlated with M. However, when an optimizer selects candidates specifically by maximizing M, conditional expectation follows the regression-to-the-mean shrinkage formula:

As selection threshold m increases, points with the highest observed M disproportionately possess large positive noise realizations ε > 0, so the true value G systematically lags behind the selected score M even without any strategic human manipulation.

2. Extremal Goodhart (Tail Distribution Shift / Out-of-Distribution Breakdown)

In the baseline operational domain around the population mean, M and G may share a strong positive linear correlation (for example, human height M correlates positively with basketball rebounding ability G across typical adult heights). However, when optimization pushes M into the far tail of the state space (several standard deviations above the historical sample range), nonlinear biological or physical constraints dominate (for example, extreme gigantism above 2.4 meters caused by pituitary pathology impairs mobility and joint health), causing the correlation between M and G to invert in the extremal regime.

3. Causal Goodhart (Confounded / Non-Causal Intervention)

Rendered rigorously via Judea Pearl's structural causal models and interventional do-calculus, Causal Goodhart occurs when M is a downstream indicator of G (G → M) or when G and M share an unobserved common confounder U (G ← U → M), rather than M being an upstream causal driver of G (M → G). In passive observational data, conditioning on M provides valid Bayesian evidence about G (P(G | M = m)). However, when a policymaker intervenes directly to force M to a target value via do(M = m)—analogous to heating a thermometer bulb with a match to raise the room temperature reading—the intervention severs the incoming causal arrows into M, leaving P(G | do(M = m)) = P(G) unchanged.

4. Adversarial Goodhart (Strategic Campbell Gaming)

When intelligent agents with distinct private utility functions are rewarded as a function of M, they actively modify the environment to maximize M at minimum personal cost, exploiting every gap between M and G (such as banks shifting liabilities out of M3, surgeons declining high-risk patients to lower surgical mortality scorecards, or reinforcement-learning agents discovering reward-hacking loopholes).

1. Perverse Bounty Schemes (The Cobra Effect): German economist Horst Siebert (2001) coined the term cobra effect after colonial bounty schemes in British India (for cobras) and French Colonial Hanoi in 1902 (where authorities paid a bounty for each severed rat tail submitted as a proxy metric M for rat eradication G). Entrepreneurial citizens responded by breeding cobras and cutting the tails off live rats before releasing the tailless breeders back into the sewers to produce more valuable offspring—increasing the pest population while maximizing bounty payouts.
2. Healthcare Report Cards and Educational Accountability: Econometric studies by David Dranove, Daniel Kessler, Mark McClellan, and Mark Satterthwaite (2003) on mandatory cardiac surgery mortality report cards in New York and Pennsylvania revealed that publicizing hospital-level 30-day mortality rates (M) led cardiac surgeons to turn away severely ill patients who would have benefited most from bypass surgery, lowering measured surgical mortality while worsening aggregate patient health outcomes (G).
3. Reinforcement Learning from Human Feedback (RLHF) and Reward Overoptimization: In modern machine learning, Leo Gao, John Schulman, and Jacob Hilton (2023) established scaling laws for reward model overoptimization, demonstrating that as a policy network is optimized via reinforcement learning or best-of-N sampling against a learned proxy reward model R_proxy (M), the true gold-standard human preference score R_gold (G) initially rises with the square root of the Kullback–Leibler divergence D_KL before peaking and declining linear-ly as the policy exploits adversarial out-of-distribution flaws in the proxy reward model.

How does Goodhart's law differ from the Lucas critique?

Goodhart's law is a broad empirical and statistical principle applicable to any regulatory target, corporate key performance indicator (KPI), or machine-learning reward function, whereas the Lucas critique is the specific macroeconomic theory explaining why reduced-form econometric relationships shift when policy rules change: rational economic agents revise their expectations and optimal decision rules in response to the new policy regime. In the Manheim–Garrabrant taxonomy, the Lucas critique corresponds primarily to Causal and Adversarial Goodhart.

Can Goodhart's law occur even when nobody is trying to cheat or game the system?

Yes. Both Regressional Goodhart (where selecting the highest values of a noisy metric M = G + ε automatically selects for positive noise ε) and Extremal Goodhart (where pushing a metric into extreme tail values leaves the region where M and G were linearly correlated) occur in purely mechanical, non-strategic statistical systems with zero human deception.

How do mechanism designers mitigate Goodhart's law in organizations?

Following Holmström and Milgrom (1991), organizations mitigate Goodhart distortion by: (1) muting incentive intensity (using lower-powered salaried compensation rather than aggressive piece-rate bonuses when important quality dimensions cannot be measured); (2) bundling balanced scorecards of complementary metrics that are harder to game simultaneously; (3) rotating or auditing metrics unpredictably; and (4) incorporating Kullback–Leibler regularization penalties (in AI alignment) to prevent policies from drifting too far from the baseline distribution where the proxy metric remains valid.

1. Goodhart, C. A. E. (1984). "Problems of Monetary Management: The U.K. Experience." In Monetary Theory and Practice: The UK Experience (pp. 91–121). Macmillan. https://doi.org/10.1007/978-1-349-17295-5
2. Lucas, R. E. (1976). "Econometric Policy Evaluation: A Critique." Carnegie-Rochester Conference Series on Public Policy, 1, 19–46. https://doi.org/10.1016/S0167-2231(76)80003-680003-6)
3. Holmström, B., & Milgrom, P. (1991). "Multitask Principal–Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design." Journal of Law, Economics, & Organization, 7, 24–52. https://www.jstor.org/stable/764957
4. Strathern, M. (1997). "'Improving Ratings': Audit in the British University System." European Review, 5(3), 305–321. https://doi.org/10.1017/S1062798700002660
5. Dranove, D., Kessler, D., McClellan, M., & Satterthwaite, M. (2003). "Is More Information Better? The Effects of 'Report Cards' on Health Care Providers." Journal of Political Economy, 111(3), 555–588. https://doi.org/10.1086/374180