What Consumer Choices Can Reveal When Shoppers Ignore Some Options

Debopam Bhattacharya of the University of Cambridge and Ryan J. Martin of Faire Wholesale study a problem that arises whenever consumers choose from less than the full market. A product may be overlooked because a buyer has not heard of it, finds searching costly or uses a narrow shopping platform. An economist observing only the eventual purchase cannot necessarily tell that apart from a strong dislike of the product.

Their paper, Unobserved Consideration and Consumer Welfare, is a theoretical analysis, not an estimate of the effects of an actual policy. It was submitted as an arXiv preprint on 5 November 2026; the landing page does not indicate journal acceptance.

What the calculation measures

The authors focus on compensating variation: the amount of money that would restore a consumer to their original level of well-being after prices change. The amount can differ across people because they value products differently and consider different alternatives. The paper studies the distribution of these amounts after each consumer’s consideration set has been realized, rather than compensation calculated before that set is known.

In their model, each person chooses their preferred option from a nonempty shortlist. Utility depends on the option and the income left after paying for it. Preferences may vary freely across consumers, income can affect choices, and preferences can be correlated with the shortlist. The analysis assumes utility is continuous and strictly increasing in remaining income, and that ties for the best option have probability zero at the relevant price and income combinations.

The crucial assumption is that each person’s shortlist and the population remain unchanged across the price and income configurations used in the calculation. Under that condition, the authors prove that the entire compensation distribution is the same function of structural choice probabilities—the probabilities of choosing each alternative at specified prices and incomes—as in an equivalent full-consideration analysis. Shortlists need not be separately identified. The distribution also yields quantities such as median and mean compensation.

The method constructs a hypothetical budget for each proposed compensation amount. For every option, it uses whichever of the original budget or the compensated post-change budget leaves the consumer more income after purchase. The option chosen at this constructed budget indicates whether that amount of compensation is enough. Summing the appropriate choice probabilities gives the share of consumers needing no more than the proposed amount.

Why missing shortlists need not obscure welfare

The authors also construct a full-consideration model that reproduces the original model’s choices and each individual’s compensation. In this representation, options originally excluded from a person’s shortlist have finite utilities that remain below those of considered options. The exercise does not show that people literally consider everything; it shows that, within the paper’s broad preference class, observed demand can be consistent with different explanations that nonetheless imply the same compensation.

That equivalence has limits. If an additional assumption guarantees that a product eventually becomes everyone’s favorite when its subsidy becomes sufficiently large, its limiting demand can reveal the fraction considering it. Such extreme price variation and the additional preference restriction are not supplied by the main result.

The practical hurdle is substantial: researchers must identify structural demand for the same population at the constructed prices and incomes, which generally differ from both the original and final market conditions. Observed purchases at one set of prices are not enough. Suitable price and income variation, appropriate controls for confounding, or defensible extrapolation may be required.

When attention changes with prices

The paper separately considers price increases that can shrink shortlists—for example, when shoppers filter out expensive products. It assumes that consideration contracts monotonically as prices rise, that an outside option is always considered, and that compensation is finite. In this setting the demand-based expression becomes an upper bound on the share adequately compensated by a given amount. An upper bound on the fraction of consumers whose shortlists change supplies a lower bound. The authors present these as sensitivity bounds, not a general proof that they are the tightest possible.

Their hypothetical clean-vehicle illustration assigns price increases of zero, $3,750 and $7,500 across options after credit withdrawal. If at most 10% of consumers lose a considered option, the model implies at least 90% need no more than $7,500 in compensation. That is a conditional mathematical illustration, not an empirical finding about vehicle buyers. Even small attrition can leave the upper tail—and mean compensation—without a finite uniform bound, because losing a highly valued option can be much more costly than the price increase itself.

An appendix extends the method to specified additions and removals of options, but requires demand under the combined menu and stable potential consideration. Across these cases, the message is not that missing information never matters: it is that the information needed for welfare may be different from the information needed to explain why consumers overlook products.