AI Glossary / Statistics and probability / Intermediate
Choice set
Definition
A choice set is the collection of alternatives available to a decision-maker for a particular decision. In a standard discrete-choice model, alternatives are defined so that the model represents a choice among a finite, mutually exclusive and collectively exhaustive set. The set can differ across people and occasions, and it is not necessarily identical to every option that exists in the market.
What it means
Choosing a product depends both on preferences and on what was available. A customer cannot select an out-of-stock item, and a commuter may lack access to a particular transport mode. Researchers also distinguish available alternatives from those a person actually considers. The analyst may observe one set imperfectly or model consideration separately. Failing to define these boundaries can make restricted opportunity look like preference. Attributes describe alternatives; they are not themselves the choice set.
How it works
Define the decision occasion, decision-maker and possible alternatives. Establish availability rules and include an outside or no-choice option when it belongs to the decision being modeled. Record the alternatives offered or accessible at the time, together with their relevant attributes. A discrete-choice model assigns probabilities conditional on that set, often using a utility specification. Some models impose particular substitution patterns when the set changes. If researchers sample alternatives from a very large set, they need estimation methods that account for that sampling rather than treating the subset as the complete market.
Three practical examples
- Product analytics: distinguish a customer's choice among displayed products from preferences over products that were never shown.
- Transport research: model feasible travel alternatives for a trip, including combinations when the decision definition requires them.
- Recommendation systems: analyze which item a user selected from the actual recommendation list, retaining exposure information rather than only the clicked item.
Think of it this way
Think of ordering from a menu. Your selection tells us something about your preferences, but only in relation to the items available and the option of ordering nothing. An item missing from the menu cannot be treated as an item you actively rejected.
Worked example
Consider an illustrative multinomial logit model with three available alternatives A, B and no purchase. Their systematic utilities are ln(2), zero and zero. Exponentiating gives weights two, one and one. Conditional choice probabilities are therefore 2/4 = 0.5 for A and 1/4 = 0.25 for each other option. If B becomes unavailable while the remaining utilities stay fixed, the probabilities become 2/3 for A and 1/3 for no purchase. The model reallocates B's probability proportionally across the remaining options. Now suppose an analyst incorrectly omits no purchase while both products are available. The model reports A's conditional share as 2/3 instead of 1/2 of all decision occasions. Neither number is inherently an arithmetic error: they answer different conditioning questions. The multinomial logit substitution pattern is a modeling assumption, not a universal law of human choice, and the stipulated utilities do not establish how actual customers respond to an availability change.
Illustrative case study
Fictional case: Meadow Commerce trains a recommendation model using only purchases and product attributes. Analysts discover that some products appear unpopular because they were rarely available or displayed. The team adds historical exposure and stock information, defines the relevant no-purchase occasions and evaluates predictions on later sessions. It also investigates whether the display policy depends on user characteristics. This fictional case illustrates the importance of choice-set information and does not claim that exposure-adjusted modeling automatically identifies causal preferences.
Common misconceptions and mistakes
The choice set is not always the same for every person. The set of feasible options may differ from the consideration set, and neither is necessarily fully observed. Alternatives must be defined at the right level: if people can choose both products, a model that permits only A or B may omit valid combinations. The attributes of alternatives need not be mutually exclusive or independent. Removing an option can change preferences or context, not merely the denominator of a probability formula. A recommender's display policy can create selection effects that complicate learning from observed choices.
Business use
Businesses should retain what was offered, when it was offered and whether it was genuinely available. Separate market-share questions from conditional choice among displayed options. In experiments, document the treatment's effect on both presentation and the set itself. Evaluate whether a model's substitution assumptions are credible before using it to forecast assortment or service changes. When an AI assistant recommends an option, make sure feasibility constraints are applied consistently and that observed nonselection is not interpreted as dislike when the user never had a real opportunity to choose.
People also ask
Is a no-purchase option always required?
It is needed when declining to choose is part of the decision being modeled; a conditional model of purchases answers a narrower question.
Can two people have different choice sets?
Yes, because availability, location, eligibility or other constraints differ.
Does choosing A prove that B was disliked?
No. B may have been unavailable, unnoticed or simply less preferred on that occasion.
Check your understanding
Q: Why does A's probability rise from one-half to two-thirds when B is removed in the worked example?
Answer: A: Under the specified logit model, the remaining exponential utility weights are two and one, so the denominator falls from four to three. That result depends on the model's assumptions.
Related terms
- Availability
- discrete choice
- alternative
- consideration set
- random utility
- multinomial logit
- outside option
- substitution and exposure bias
Learn next
list the alternatives for a familiar decision and check whether combinations or an outside option are missing. Recalculate the example after changing availability, then study why nested or mixed choice models can imply different substitution patterns from simple multinomial logit.
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Sources
Sources: Kenneth Train, Discrete Choice Methods with Simulation, choice-set requirements and model interpretation: https://eml.berkeley.edu/books/train1201.pdf ; UC Berkeley, discrete-choice framework and alternatives: https://its.berkeley.edu/publications/extended-discrete-choice-models-integrated-framework-flexible-error-structures-and ; Tomlinson, Ugander and Benson, “Choice Set Confounding in Discrete Choice,” research on exposure and selection: https://arxiv.org/abs/2105.07959 .
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