In the late 1970s, Richard Feynman turned a lunch dilemma into a math problem: over a fixed number of meals, when should you stop trying new dishes and settle on the best one you've found? A new paper in PNAS by Brian Christian, Evan Russek, and Tom Griffiths deciphers Feynman's handwritten notes, proves his threshold solution optimal, extends it to other value distributions, and tests a restaurant version of the problem on 2,520 participants. People behave in a manner that is unusually consistent with Feynman's predictions: they use thresholds that fall linearly with the proportion of nights remaining, shift the intercept when the distribution of restaurant quality changes, and score nearly as well as the optimal policy. Impressive stuff. I'll be honest, I'm a huge fan of Evan and Tom's work and I really enjoyed reading this piece.
However, when we think about what this tells us about planning agency and complex decision-making, we should pause. Notice what participants were given. The options were a 4-by-7 grid of restaurants on a screen. The temporal horizon was announced up front. The quality distribution was shown in advance (84 samples). Every option had a single stable score, revealed on the first visit. All that remained open was timing: try something new tonight, or go back? The authors are clear that the task abstracts from real dining. I'm not trying to nail them on that fact; instead, I want to think about what this abstraction obscures.
Wayne Wu's Movements of the Mind (2023, Oxford) offers a vocabulary for saying what kind of problem this is. On Wu's picture, action happens inside a behavior space, a branched structure of possible couplings between inputs (perceivings, rememberings, thoughts) and responses. To act is to solve a Selection Problem: one path among many gets instantiated, and attention just is the selecting. An optimal stopping task is a Selection Problem in close to pure form. The space comes ready-made, each night offering the same fork: explore or go back. Read this way, the PNAS result shows that human beings are excellent path-selectors within a constructed decision space.
The prior problem is how that space gets built. The real world doesn't have researcher-constructed grids floating around. Whether tonight is a restaurant night at all depends on plans that have nothing to do with food; which restaurants count as live options shifts with budget and company; the "horizon" is endlessly malleable. I've argued that the capacity implicated in this earlier stage of the planning process (the construction of decision space) is vigilance*.* This is not a form of attention--as Wu and other cognitive psychologists claim--but a distinctive feature of our planning agency. Our plans are characteristically partial (e.g., I'll spend more time practicing Spanish next month, I've gotta get around to writing that paper for the conference, etc.). Something has to fill those partial plans in: sustaining dormant commitments, bringing relevant plans to mind at the right time, and so on. That capacity is what assembles and maintains the option sets that selection then runs over. And it is a computationally different beast from optimal stopping. Stopping problems are well-posed, with a known distribution, a fixed horizon, one currency of value, and discrete moves. Construction is not well-posed. Its failures aren't failures of timing, stopping too early or too late; they're the highway exit you blow past while singing your favorite song, the meeting you accept that overlaps with your daughter's soccer game, and so on.
Christian, Russek, and Griffiths draw a resource-rationality moral: a linear rule of thumb captures nearly everything the optimal policy delivers. I'd push it a step further. If the in-task problem is that cheap, then the computational action in everyday decision-making lies mostly elsewhere, upstream, in whatever poses the problem, such as settling that tonight is a restaurant night at all. Optimal stopping is the tractable tail end of practical reasoning, but it is optimized partly because somebody else is doing all the hard work of constructing the decision space. To that end, you might find it curious that people's clearest departure from their own linear rule is extra exploration in the early nights. That makes perfect sense if participants are not treating the option set as fixed. That is, in the earlier stages, some people might be oscillating between constructing a decision space and selecting within it. In any case, a full-blown theory of human decision-making will need to understand both the construction of and selection within decision spaces.