Survival of the Fittest or the Luckiest? When Evolution Meets Goodhart's Law
> Original paper: *Selection of the fittest or selection of the luckiest: the emergence of Goodhart's law in evolution* > Authors: Bastien Mallein, Francesco Paparella, Emmanuel Schertzer, Zsófia Talyigás > Source: arXiv:2503.21849 [q-bio.PE], March 2025 > Method: Simulations and mathematical analysis based on an idealized evolutionary model
1. The Trap of Exam Scores
Imagine a high school where the principal makes the average exam score the only evaluation metric. Under pressure, teachers optimize not teaching but scores: fewer hard problems, endless drilling, test-taking techniques as required coursework. Three years later, average scores have risen, but creativity, critical thinking, and curiosity have declined.
This phenomenon has a name in economics—Goodhart's Law. In 1975, British economist Charles Goodhart, then an advisor to the Bank of England, observed while studying UK monetary policy: "Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes."
Two decades later, anthropologist Marilyn Strathern popularized it in one sentence:
> "When a measure becomes a target, it ceases to be a good measure."
Goodhart's law runs through education, healthcare, finance, and scientific evaluation. Now, a group of mathematicians and biologists has found that evolution itself cannot escape it.
2. Evolution's Engine: Natural Selection
In 1859, Darwin proposed natural selection: in a resource-limited world, individuals better adapted to their environment are more likely to survive and reproduce, shifting populations toward the "better." Intuition suggests stronger selection pressure—harsher environments, fiercer competition—should speed up evolution.
In 2017, Otsubo and colleagues challenged this in *PLOS ONE*: in recombination-driven evolution (where genetic variation comes mainly from recombination rather than mutation), overly strong selection actually slows evolution—like a sieve whose mesh is too fine, clogged by sand. Individuals become "too good" and reject foreign genes, killing recombination opportunities.
Mallein et al. went further, asking: what is this "too much selection is harmful" phenomenon, fundamentally?
The answer: Goodhart's law.
3. When Fitness Becomes the Target
In their model, individuals carry different genotypes, each with a fitness—the ability to survive and reproduce. But fitness is a property of the phenotype, which is shaped not only by genes but by countless random factors: timing of mutations, small environmental fluctuations, chance encounters. In other words, the fitness signal seen by selection is a mix of true genetic advantage and random luck.
Under mild selection, this signal mostly reflects real genetic differences. But Mallein et al. found a threshold effect:
> As selection pressure increases, adaptation speeds up—only up to a critical point. Beyond it, further pressure yields no more adaptation; instead, random effects (luck) dominate who reproduces.
Two consequences follow: 1. Adaptation rate drops sharply—the population is trapped at local optima 2. Genetic diversity collapses—randomness erases genetic differences, homogenizing the population
A biological version of Goodhart's law: fitness, a metric meant to measure individual quality, stops faithfully reflecting genetic quality once selection pressure makes it the sole filtering criterion. Luck—the thing evolution was supposed to eliminate—becomes decisive.
4. Mathematical Elegance: A Phase Transition in Traveling Waves
The mathematical explanation is elegant. The authors map evolution onto the Fisher-KPP equation (named for Fisher, Kolmogorov, Petrovskii, and Piskunov), a foundational equation for population spread and reaction-diffusion processes.
Population expansion takes the form of traveling waves of two basic types:
- Pulled waves: wave speed determined by linear analysis of the leading edge, as if pulled by a few vanguard individuals
- Pushed waves: wave speed determined by internal nonlinear dynamics, as if pushed by the collective
- Education: Teaching to the test raises scores while destroying learning.
- Healthcare: Optimizing patient-satisfaction scores leads doctors to avoid difficult cases; ratings rise, real quality falls.
- Finance: Optimizing risk models led banks to package assets to be invisible to those models—2008 was a catastrophic demonstration.
- Science: Chasing citations and h-indices encourages hot topics, avoids risky exploration, and incentivizes manipulation; papers multiply while breakthroughs thin out.
- Management: Quarterly-earnings targets drive R&D cuts, buybacks, and accounting games—short-term numbers shine while long-term competitiveness erodes.
- Goodhart, C. A. E. (1975). "Problems of Monetary Management." *The Reserve Bank of Australia*.
- Strathern, M. (1997). "'Improving ratings': audit in the British University system." *European Review*.
- Gould, S. J. (1989). *Wonderful Life: The Burgess Shale and the Nature of History*.
- Otsubo, Y., et al. (2017). "Stronger selection can slow down evolution driven by recombination." *PLOS ONE*.
- Mallein, B., et al. (2025). "Selection of the fittest or selection of the luckiest." arXiv:2503.21849.
The key insight: when selection pressure crosses a critical value, the system undergoes a phase transition from a pushed wave to a pulled wave. In the pulled regime, the leading edge is dominated by a tiny minority of front-runners whose success is largely random—so the whole population's evolutionary direction is hijacked by random fluctuations at the front.
It's like an army on the march: under moderate pressure, speed depends on the organization and strength of the whole; at maximum pressure, only the point scouts decide the direction—and they may simply be those who happened to surge ahead, not necessarily the best soldiers.
5. Historical Contingency: Gould's "Replaying the Tape"
In 1989, paleontologist Stephen Jay Gould published *Wonderful Life*, with its famous thought experiment:
> "Replay the tape of life a million times... I doubt that anything like *Homo sapiens* would ever evolve again."
Gould argued evolution is contingent: history does not march toward an optimum but is woven from unrepeatable small events. His view long remained controversial, with many believing natural selection's deterministic force was strong enough to overwhelm chance. Mallein et al.'s work provides mathematical support: when selection pressure is too strong, contingency is not suppressed but amplified.
This doesn't mean selection is unimportant—without it, evolution wouldn't happen. But selection has an "optimal dosage," like a drug: too little is ineffective; too much is toxic.
6. From Evolution to Society: Goodhart's Law Everywhere
The finding resonates far beyond biology:
In all these cases, the metric was originally created to measure something important. Once it became the target, people optimized the metric itself. The gap between metric and goal is where Goodhart's law lives.
7. What Can We Learn?
1. Stronger selection is not always better. There is an optimal intensity for any filtering mechanism—in education policy, talent selection, or performance reviews, don't make the sieve's mesh too fine. 2. Distinguish signal from noise. Fitness is an estimate of genetic quality that always contains randomness. Treating it as absolute means treating noise as signal. Good mechanism design amplifies signal and suppresses noise—not the reverse. 3. Diversity is the fuel of evolution. The most insidious harm of Goodhart's law is silently destroying diversity. When everyone optimizes the same metric, the system loses the ability to explore alternatives—whether in gene pools, marketplaces of ideas, or innovation ecosystems. 4. Face complexity with humility. Jacques Monod wrote in *Chance and Necessity* that "chance alone stands at the very source" of evolution. The mathematics turns that poetic observation into a rigorous insight: we cannot—and should not try to—eliminate chance from complex systems.
Conclusion: Between Metrics and Meaning
"Survival of the fittest" is so concise and powerful that we forget to ask: what is "fit," and who defines it? If "fit" is an oversimplified metric, pursuing it may mean the fit no longer survive.
Evolution has spent four billion years demonstrating that the most successful systems are not those that filter most strictly, but those that maintain a delicate balance between deterministic forces and random exploration. Perhaps human society should learn something from this oldest of teachers.
After all—whether DNA sequences or KPI spreadsheets—when a measure becomes a target, it ceases to be a good measure. Even evolution itself cannot violate this rule.