Estimating consumer preferences is central to many problems in economics and marketing. This paper develops a flexible framework for learning individual preferences from partial ranking information by interpreting observed rankings as collections of pairwise comparisons with logistic choice probabilities. We model latent utility as the sum of interpretable product attributes, item fixed effects, and a low-rank user-item factor structure, enabling both interpretability and information sharing across consumers and items. We further correct for selection in which comparisons are observed: a comparison is recorded only if both items enter the consumer's consideration set, inducing exposure bias toward frequently encountered items. We model pair observability as the product of item-level observability propensities and estimate these propensities with a logistic model for the marginal probability that an item is observable. Preference parameters are then estimated by maximizing an inverse-probability-weighted (IPW), ridge-regularized log-likelihood that reweights observed comparisons toward a target comparison population. To scale computation, we propose a stochastic gradient descent (SGD) algorithm based on inverse-probability resampling, which draws comparisons in proportion to their IPW weights. In an application to transaction data from an online wine retailer, the method improves out-of-sample recommendation performance relative to a popularity-based benchmark, with particularly strong gains in predicting purchases of previously unconsumed products.
Estimating consumer preferences is a foundational task in economics. Preference estimates are central inputs to structural demand and discrete-choice models that quantify substitution patterns and willingnessto-pay, enabling counterfactual evaluation of pricing, assortment, and new-product decisions (McFadden, 1973;Train, 2009). They also underpin stated-preference methods such as conjoint and choice experiments, which remain workhorse tools for product design, positioning, and market simulation when historical sales data are limited or unavailable (Green and Srinivasan, 1990;Louviere, Hensher, and Swait, 2000). In digital marketplaces, learning preferences at the individual level is equally critical for personalization: recommender systems, search ranking, and targeted promotions , often leveraging latent-factor representations and pairwise ranking objectives (Koren, Bell, and Volinsky, 2009;Koren, Rendle, and Bell, 2021). 1 arXiv:2602.16476v1 [stat.ML] 18 Feb 2026 This paper develops a new approach to learning individual preferences from ranking data. We consider settings in which researchers observe how consumers rank subsets of available options, rather than complete orderings over the entire choice set. Such ranking data may be obtained directly from surveys that ask respondents to compare or rank alternatives, or indirectly inferred from revealed preference in observed choices. For example, if a consumer chooses item j when item j ′ is also available, this choice reveals that j is preferred to j ′ . Crucially, we do not assume that researchers observe a complete ranking over all items for any individual. Instead, the central objective of this paper is to recover consumers' underlying preference structures-and, in particular, to infer rankings over unobserved item pairs-using only partial and incomplete ranking information observed across individuals.
The proposed approach learns individual preferences by exploiting two complementary sources of information. First, preferences can be inferred from how consumers rank items with different observable attributes. Rankings among observed items reveal consumers’ tastes over product characteristics, which can then be extrapolated to items that have not been directly ranked. For example, if a consumer systematically ranks Brand A above Brand B among the items she evaluates, this pattern suggests that products sharing Brand A’s attributes are likely to be preferred.
Second, the approach leverages similarities in observed rankings across consumers. When two consumers exhibit similar ranking patterns over a subset of items, information about one consumer’s preferences can inform about the other’s unobserved comparisons. In particular, if two consumers share closely aligned rankings on a common set of items and one consumer is observed to prefer item A to item B, it is more likely that the other consumer also prefers item A to item B. By combining attribute-based extrapolation with cross-consumer similarity, the method pools information efficiently to recover preferences beyond the directly observed rankings.
To operationalize these ideas and estimate preferences, we model consumers’ latent utility and interpret the observed ranking data as a collection of pairwise choice comparisons. The utility of an item is decomposed into an interpretable component that captures systematic preferences over observable product attributes-such as brand or country of origin-and a latent factor component that captures residual similarities between users and items not explained by these attributes. This structure allows the model to combine both attribute-based extrapolation with information pooled across consumers who exhibit similar ranking patterns. Estimation proceeds by viewing each observed ranking as the outcome of a hypothetical binary choice. When item A is observed to be ranked above item B for a given consumer, we interpret this as evidence that the consumer would choose A over B if both items were simultaneously available. To map this interpretation into an estimable likelihood, we impose the standard assumption that the idiosyncratic utility term follow a type-I extreme value distribution. Under this assumption, the probability that item A is preferred to item B takes a logistic form, and preference estimation reduces to a binary response problem with a logistic specification. Because the number of implied pairwise comparisons can be very large, we estimate the model using a stochastic optimization procedure: in each iteration, we randomly sample a subset of observed ranking pairs and update the parameters using gradient-based steps in the spirit of stochastic gradient descent. This approach enables scalable estimation while efficiently exploiting the information contained in large and sparse ranking datasets.
We illustrate the proposed approach using transaction data from an online wine retailer. We begin by aggregating individual wine products into interpretable ca
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