Building rational surrogates

16 Nov 2025

An entity walks into the store. It sees two soft drinks. It buys the Vanilla Coke. If we see it making this choice consistently we could infer Vanilla Coke is its most-preferred soft drink. Other regularities in its choices may inform us about its rankings of other soft drinks. To draw these inferences we assume the entity is “economically rational”: it can consistently produce a transitive ranking of all options it might be presented with, and would choose the highest-ranked option every time.¹

If it is economically rational, then we can use the observed regularities to predict its soft drink choices in new settings. We don’t even have to pretend we know everything it considers in making the choice. Good predictions tell us we have captured enough salient features driving its soft drink choices. Bad predictions tell us we either need more observations or data on factors it may consider. Either way, within the rational choice framework we maintain the assumption that its choices reflect a complete and transitive ordering over options.

Suppose the entity is not rational; suppose it chooses at random among the options it can afford. Perhaps it flips a coin before every decision and buys the item on the left if heads. Everything else—packaging, mood, habit—is, but for random correlations with its budget constraint, irrelevant. The budget constraint will still generate a downward-sloping demand curve so our machinery can still work, predictively. With a large enough sample, perhaps we learn that most non-price variables don’t improve predictions much. But even supermarket scanner data linked to credit card statements and cell phone movement patterns say little about the coin, so perhaps not. What, then, do we learn by fitting a rational choice model to its behavior?

Literally making up a guy

To fit a rational choice model is to construct the preferences of a surrogate agent who would have made many of the same choices as the people in the data. The better the surrogate, the better it reproduces the joint distribution of choices. The surrogate is more restricted than the underlying entities, since its choices must be economically rational given what’s in the model while reflecting the idiosyncratic preferences of the actual entities as best it can. The art of building a good rational surrogate is partly the art of shaping what’s in the model, i.e., what the surrogate sees and how it sees it.

The rational surrogate also takes up less space and time than going full Diaconis Holmes Montgomery on the actual entity’s coin and hands. Instead of lugging around a giant lookup table of observed choices, we carry a projection of observed choices onto a more tractable “rational” subspace. We may choose between rational projections and subspaces based on statistical or theoretical criteria, aesthetics, or something else.²

That is, rational choice modeling is just a structured way to make up a guy. Why would we want to make up a guy? Because we can predict the rational surrogate’s behavior, design products the rational surrogate is more likely to buy, even reason about the rational surrogate’s well-being better than we can for the underlying entities. It helps that rational surrogates sometimes predict people’s behavior pretty well. So what did we learn by the fitting exercise? Unclear, but it will appear we gained something that helps us make plans and shape behavior.

To the extent that the statistical regularities captured in a rational surrogate predict behavior well out of sample, it seems reasonable to think of economic rationality as a compression scheme. Rational preferences describe the constrained-best way to achieve some set of goals. In some regimes, approximations and heuristics may be more space-time efficient than an exact analytic maximizer.³ I find this line of thought interesting but not, by itself, practically useful.

My preferences; Our rational surrogate

Historically, it’s been tough to construct a general rational surrogate for a person purely from their own data.⁴ This seems to be a pretty active area (e.g., 1, 2) so I’m sure much more is possible than what I recall from seminars and literature/scrolling. But most of what I’ve seen in public involves building rational surrogates from data on the choices of groups of people. The statistical models can allow for quite flexible group structures, such that the surrogates reflect relatively similar types of people (within the context of the model).

The computational machinery that lets you construct our rational surrogate will “work” no matter how poorly your chosen subspace reflects what I actually see and consider, let alone anyone else “like me”. Is it good that you can make up a guy who is, for analytical purposes, “kinda like me” in whatever ways you can conceptualize me? Even the notion of “like” is entirely defined by your modeling choices and ability to recognize who and what I am. Your out of sample predictions may be garbage but who will force you to score them?

These concerns seem perhaps prosaic in business settings where competition and external feedback are strong and push rational surrogates to accurately reflect factors relevant to consumer behavior. Variables related to budget constraints and purchase histories⁵ are generally measured well enough, or can at least be defined well enough, to enable the development of decent rational surrogates. You can even make a bunch of them, shove them all in a linear regression, and let the gods sort it out.

These concerns seem perhaps more pointed in settings where competition is thin and external feedback is scarce. Then many rational surrogates can coexist, each to some degree internally consistent and mutually incompatible with the others. Worst may be when data on the factors that people consider are scarce, so that estimates of how well the rational surrogates approximate their targets are noisy. Data-driven procedures to construct rationality in settings like this are often cursed: not only is it hard to approximate the target’s compression scheme well, the signals you get can steer you away from doing better.

Rational surrogates are Procrustean beds

So what’s an organization to do when rational surrogates are cursed? Building models to faithfully represent actual entities is hard. Entities change faster than models can, and entities worth modeling are often richer than compression schemes can fully capture. But without explicit models of the target entities as goal-driven constrained actors, large organizations may be left entirely at the whims of managerial personalities and vibes or outdated folk knowledge. The most effective strategies seem to involve making your target population act more like the rational surrogates you can actually construct. Alas, rational surrogates are not built to live in worlds full of behaviorally rich entities; Procrustes has his work cut out for him.