La formule optimale d'arrêt de Feynman prédit comment nous choisissons le dîner

A 2021 study with 2,520 participants shows that people’s restaurant‑choosing behavior matches Richard Feynman’s optimal stopping formula.

Feynman’s Original Problem

Feynman, then a Caltech physicist, scribbled a threshold on a napkin during a Thai‑restaurant visit in the late 1970s. He reduced the dilemma—whether to stick with a known favorite or risk a new dish—to a stopping problem in decision theory. His solution involved a square‑root threshold that tells diners when the expected gain from trying new food drops below the value of the best dish so far.

Experimental Validation

Fast‑forward to 2021, cognitive scientists Tom Griffiths (Princeton) and Brian Christian (Berkeley) teamed with psychologist Evan Russek (City University of New York) to test the math. They built an online game that mimicked a 1‑to‑4‑week stay in a new city, letting players earn points between 1 and 100 for each restaurant choice. Participants were nudged to maximize total points. Results matched the theory. As the simulated trip neared its end, players increasingly chose the best prior restaurant, mirroring the square‑root cutoff. Even without knowing the formula, participants’ risk‑aversion patterns aligned closely with Feynman’s prediction. Shoham Choshen‑Hillel (Hebrew University) praised the experiment as a “super creative article” that demonstrates how abstract math can predict real‑world choices.

Implications Beyond Dinner

This study also extended Feynman’s model. Researchers solved a generalized version that accounts for varying time horizons and reward distributions, offering a more flexible tool for any scenario where one must decide whether to keep searching or settle. While the original problem ignores boredom, the generalized framework can incorporate it, making it relevant for marketing, real‑estate, and even algorithmic recommendation systems. What this means for engineers is that optimal stopping theory isn’t just a textbook curiosity. It can inform the design of adaptive interfaces that balance exploration and exploitation, or the tuning of recommendation engines that must decide when to surface new content. By embedding a simple square‑root rule, systems can mimic human intuition and improve user satisfaction without heavy computation. Future work will likely test the model in more complex, noisy environments—like fluctuating restaurant quality or multi‑attribute choices. For now, the 2,520‑participant experiment confirms that even casual diners follow a mathematically optimal strategy, and that the same rule can guide smarter, data‑driven decision systems.

Source: How math can help you decide what to order for dinner
Domain: scientificamerican.com