CALIFORNIA — Researchers published a study in the Proceedings of the National Academy of Sciences reconstructing and testing Richard Feynman’s unpublished mathematical model for optimally choosing restaurants during a multi-night stay in a city. Feynman had devised an equation to address the dilemma of when to stop searching for a better restaurant while visiting a city for a known number of nights.
Feynman developed the model after a lunch in the 1970s with his friend Ralph Leighton at a Thai restaurant in California, where Leighton debated whether to stick with his favorite ginger chicken or try a new dish. Feynman turned the restaurant choice issue into a mathematical problem, but his work remained in handwritten notes that were not formally published. Those notes went undeciphered for decades until researchers reconstructed his original problem and solution.
The researchers reframed Feynman’s original dish-selection dilemma as a restaurant-selection problem over multiple nights. In his model, a diner should try a different restaurant each night until finding one that exceeds a quality threshold that declines as the number of remaining nights decreases. The threshold drops more rapidly as fewer nights remain. The model assumed that any restaurant within a fixed range of quality is equally likely to be encountered.
To test human behavior against Feynman’s approach, researchers recruited 2,520 participants for an online task in which they imagined dining in a city for varying durations and selected restaurants from a grid representing different quality levels. Once a participant selected a restaurant, its quality was revealed. The study found that participants’ decision thresholds decreased linearly with the proportion of nights remaining, rather than declining more rapidly as in Feynman’s model.
“The essence of the problem is that the value of exploring, of looking around and trying something new, decreases the opportunities you’re going to have to make use of that information,” said Tom Griffiths, professor at Princeton University. “The thresholds are being guided by the best thing you might be able to find if you kept looking. If you have a long time to look, finding something amazing has a lot of value because you can go back many times.” Griffiths added, “It’s a little bit simpler than Feynman’s solution, but it actually turns out to be quite good. The trick is having a threshold and then decreasing that threshold as you get closer to the end [of a trip]. And as long as you are doing something like that, that’ll actually work pretty well.”
The researchers also showed that if the distribution of restaurant quality varies, the optimal strategy changes accordingly. In areas with mostly poor restaurants and a few exceptional ones, the initial quality threshold should be higher, justifying longer exploration. In areas where most restaurants are of similar, above-average quality, the threshold is lower, making extended exploration less valuable.