📈 economics

Distilling Models of Bounded-Rational Choice: A Constraint Programming Approach

This paper introduces a constraint programming framework to distill the explanatory and welfare-relevant content of computationally hard bounded-rational choice models, demonstrating that limited-attention models effectively explain human behavior while new selection criteria significantly reduce their predictive indeterminacy.

Original authors: Özgür Akgün, Georgios Gerasimou

Published 2026-07-07

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Özgür Akgün, Georgios Gerasimou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Why Do We Need This Paper?

Imagine you are watching someone choose a meal from a menu. If they are a "perfectly rational" person, they have a single, clear list of favorites (e.g., Pizza > Burgers > Salad) and they always pick the best item on that list. This is the standard "Rational Choice" model economists usually use.

But in real life, people aren't perfect. Sometimes they pick the salad over the pizza, even though they usually love pizza. Why?

Shortlisting: Maybe they first decided, "I'm not eating anything with cheese," so they eliminated the pizza and burgers immediately, then picked the salad from what was left.
Limited Attention: Maybe the menu was so huge they only looked at the first three items, missed the pizza, and picked the salad.

For decades, economists have built complex mathematical models to describe these "imperfect" behaviors (called Shortlisting and Limited Attention). The problem? These models are so flexible that they can explain almost anything. If you see a weird choice, you can usually invent a story (a specific set of rules or a specific "blind spot") that makes it fit.

Because these models are so flexible, they are hard to test. It's like having a detective who can solve any crime by making up a new suspect for every case. You can't tell if the detective is smart or just making things up.

This paper introduces a new tool to solve that problem. The authors use a type of computer science called Constraint Programming to act like a super-efficient filter. They don't just ask, "Can this model explain the data?" They ask, "What is the best explanation, and how many different explanations are there?"

The Tools: The "Smart Search Engine"

The authors use two main computational tricks to tame these messy models:

Constraint Programming (CP): Imagine you are trying to find a specific key in a giant, dark room full of millions of keys. A normal search would check every single key one by one (brute force). CP is like having a robot that knows the shape of the keyhole. It instantly eliminates every key that is too big, too small, or the wrong shape, narrowing the search down to just a few candidates. This allows the computer to handle the massive complexity of these models without crashing.
Constraint Dominance Programming (CDP): This is the "quality control" step. Imagine you find 1,000 keys that fit the lock. That's too many to choose from. CDP helps you throw away the "worse" keys.
- The Rule: If Key A fits the lock and is more similar to a "perfect" key than Key B, we throw Key B away.
- The Goal: They want to find the explanations that are closest to "perfect rationality." If a person is mostly rational but made a small mistake, we want to find that story, not a story where they are completely chaotic.

The Experiment: The "Knitting Dress" Test

To test their new tools, the authors looked at data from two real experiments involving people choosing knitted items (dresses and ponchos).

The Setup: People were shown groups of items (menus) and asked to pick one.
The Findings:
- Most people were actually quite rational. About 70-90% of the choices could be explained by a simple "I like this best" list.
- For the rest: The "Limited Attention" models (where people ignore some items) explained the weird choices better than the "Shortlisting" models (where people eliminate items based on rules).
- The Catch: The Limited Attention models were too good. They were so flexible that they could explain random guessing just as well as real choices. It was like a detective who could solve a crime even if the suspect was innocent.

The "Indeterminacy" Problem: Too Many Answers

Here is the most surprising part of the paper. Even after using their "quality control" filters to find the best explanations, there were still too many of them.

The Analogy: Imagine you are trying to guess a friend's secret password.
- Rational Choice: There is usually only one password that fits the clues.
- Bounded Rationality (Shortlisting/Attention): Even after filtering out the bad guesses, you might still have thousands of passwords that fit the clues perfectly.

The authors found that for the "Limited Attention" models, there were often thousands of different "stories" (combinations of rules and blind spots) that could explain a single person's choices. This is called indeterminacy. It means that even if the model fits the data perfectly, we still don't know why the person made that choice. We know that they were limited in attention, but we don't know exactly which items they ignored.

The "Randomness" Check

To see which models were actually useful, the authors ran a "lie detector" test. They asked: "Could a person who is just guessing randomly (like flipping a coin) have made these choices?"

The Result: The "Limited Attention" models were so flexible that they could explain random guessing almost as well as real human choices. This makes them less trustworthy for predicting behavior.
The Winner: The "Shortlisting" model, specifically the version where the rules are logical and consistent (transitive), was the only one that could explain the data without also explaining random guessing. It was the most "honest" model.

The Bottom Line

The paper concludes with a trade-off:

Complexity vs. Clarity: The more complex models (Limited Attention) explain more of the weird choices we see in real life.
The Cost: Because they explain so much, they are also very vague. They leave us with thousands of possible reasons for a choice, making it hard to know what is actually driving the decision.
The Recommendation: If you want to understand a person's true preferences (their "welfare"), the simpler, more structured models (like Rational Choice or logical Shortlisting) are often better. Even if they don't fit the data perfectly, the few answers they give are much more reliable than the thousands of vague answers the complex models provide.

In short: The authors built a super-smart computer filter to test how well we can understand imperfect human choices. They found that while we can explain almost anything with complex rules, the "best" explanation is often the simplest one that doesn't also explain random noise.

Technical Summary: Distilling Models of Bounded-Rational Choice: A Constraint Programming Approach

1. Problem Statement
The paper addresses a critical gap in the literature on bounded-rational choice theory. While influential models such as the "Rational Shortlist Method" (RS) by Manzini and Mariotti (2007) and "Choice with Limited Attention" (CLA) and "Overwhelming Choice" (OC) by Masatlioglu et al. (2012) and Lleras et al. (2017) have been extensively studied theoretically, they remain under-tested empirically in their full generality. The primary obstacles are:

Computational Intractability: The space of behavioral primitives (preferences and attention filters) grows exponentially with the number of alternatives, making brute-force enumeration of compatible models impossible for standard datasets.
Non-Identification: These models are generally not identified; a single dataset can be explained by thousands of distinct model instances (different preference orderings and filters), making welfare inference (determining the decision maker's underlying preferences) indeterminate.
Lack of Welfare-Relevant Distillation: Existing empirical tests often rely on "pass-or-fail" axiomatic checks. There is a lack of tools to distill the full explanatory and welfare-relevant content of these models, specifically to identify which compatible primitives are most plausible for welfare analysis.

2. Methodology
The authors introduce a computational framework utilizing Constraint Programming (CP) and Constraint Dominance Programming (CDP) to overcome the computational and identification challenges.

Constraint Programming (CP): Instead of standard optimization, the authors model the problem using decision variables (representing relations like preferences and filters), their domains, and logical constraints derived from the choice data. They utilize the Essence language, Conjure, and Savile Row to translate high-level economic models into solver-optimal inputs for the Minion solver.
- Mechanism: CP uses inference (constraint propagation) to prune the search space by ruling out variable values that cannot satisfy constraints, avoiding brute-force enumeration.
- Application: This allows the calculation of "distance scores" (analogous to the Houtman-Maks score) for models, representing the minimum number of choices that must be dropped for a model to fit perfectly. It also enables the enumeration of all primitives achieving a specific score.
Constraint Dominance Programming (CDP): To address non-identification, the authors introduce dominance-based refinements.
- Dominance Criteria:
  - For RS: An instance $(\succ^a_1, \succ^a_2)$ dominates $(\succ^b_1, \succ^b_2)$ if the relations in $a$ are supersets of those in $b$ (i.e., more complete/rational).
  - For CLA/OC: An instance $(\Gamma^a, \succ^a)$ dominates $(\Gamma^b, \succ^b)$ if they share the same preference ordering but $\Gamma^a$ considers at least as many alternatives as $\Gamma^b$ in every menu (i.e., less restrictive attention).
- Mechanism: CDP integrates these dominance relations directly into the search process. When a solution is found, the solver adds a "blocking constraint" to exclude any future solutions dominated by the current one. This avoids the inefficient "generate-and-test" approach of enumerating all solutions and filtering later.
Predictive Success Measures: The authors employ Selten's (1991) measures (difference and ratio) to compare model performance against random choice behavior (Bronars, 1987), assessing both explanatory power and permissiveness.

3. Key Contributions

Methodological Innovation: The paper is the first to apply CP and CDP to the full generality of RS, CLA, and OC models. It provides a tool chain that allows for the enumeration of all compatible primitives and the distillation of undominated (welfare-relevant) primitives.
Welfare Refinement: It proposes normative refinements that select model instances "closest" to Rational Choice (RC). For RS, this means favoring more complete preference relations; for CLA/OC, it means favoring larger consideration sets.
Empirical Framework: The authors demonstrate how to move beyond binary pass/fail tests to quantify model proximity to data, enumerate solution sets, and assess predictive success against random behavior.

4. Empirical Results
The framework is applied to two datasets from Manzini (2023): "Four Dresses" (4 alternatives, 11 menus) and "Five Ponchos" (5 alternatives, 16 menus).

Explanatory Power:
- CLA and OC (limited-attention models) explain a significantly higher proportion of subjects' choices perfectly compared to RS (shortlisting). In the "Five Ponchos" dataset, CLA explains 100% of subjects perfectly.
- However, limited-attention models are also more permissive, meaning they are more likely to explain random choice data (high "area" in Selten's ratio).
- RS (particularly the transitive subclass, $RS_{order}$ ) explains fewer subjects perfectly but is less permissive.
Indeterminacy and Parsimony:
- Non-Identification: Without refinement, the number of compatible primitives is massive (e.g., thousands for CLA in the 4D dataset).
- Effect of Refinement: The dominance criteria drastically reduce the set of primitives. In the 4D dataset, 83.3% to 99.6% of compatible instances were discarded as dominated.
- Parsimony Trade-off: Despite refinement, bounded-rational models generally yield more compatible primitives (higher indeterminacy) than Rational Choice (RC). For subjects only approximately fitting RC, the number of compatible preference orderings is typically unique or very small (median 1), whereas bounded-rational models often leave multiple undominated primitives.
Robustness to Randomness:
- Using Bronars' test, the authors find that most approximate fits of RC and perfect fits of $RS_{order}$ survive the "non-randomness" check.
- Conversely, perfect fits of CLA and OC often fail this check, suggesting their high explanatory power may stem from over-permissiveness rather than capturing genuine behavioral structure.

5. Significance and Claims
The authors position this work as a methodological contribution to behavioral revealed preference analysis. They claim that:

Computational Feasibility: CP/CDP makes it possible to analyze complex, non-parametric bounded-rational models in full generality, a task previously deemed computationally prohibitive.
Distilling Welfare Content: The framework allows researchers to "distill" the welfare-relevant content of these models by filtering out dominated primitives, thereby alleviating indeterminacy.
Trade-off Identification: The analysis highlights a fundamental trade-off in modeling imperfectly rational behavior: models with higher explanatory power (like CLA) often suffer from greater indeterminacy and lower parsimony compared to the standard rational choice model.
Future Direction: The paper does not claim to definitively solve the identification problem but argues that these tools enable a new generation of model selection that explicitly evaluates the trade-offs between explanatory power, indeterminacy, and computational complexity. The authors emphasize that while their methods facilitate deeper inquiry, the final selection of a model for welfare analysis still requires analyst discretion.