# Decision Forest: A Nonparametric Approach to Modeling Irrational Choice

arXiv: https://arxiv.org/abs/1904.11532 · HTML: https://mlsanity.com/paper/1904.11532/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2019.

## Built on by (most cited first, 11 of 11)

- [Representing Random Utility Choice Models with Neural Networks](https://mlsanity.com/paper/2207.12877/) (2022)
- [Transformer Choice Net: A Transformer Neural Network for Choice Prediction](https://mlsanity.com/paper/2310.08716/) (2023)
- [Deep Learning for Choice Modeling](https://mlsanity.com/paper/2208.09325/) (2022)
- [A Neural Network Based Choice Model for Assortment Optimization](https://mlsanity.com/paper/2308.05617/) (2023)
- [On the estimation of discrete choice models to capture irrational customer behaviors](https://mlsanity.com/paper/2109.03882/) (2021)
- [A Nonparametric Approach with Marginals for Modeling Consumer Choice](https://mlsanity.com/paper/2208.06115/) (2022)
- [Modeling Choice via Self-Attention](https://mlsanity.com/paper/2311.07607/) (2023)
- [Tight Mixed-Integer Optimization Formulations for Prescriptive Trees](https://mlsanity.com/paper/2302.14744/) (2023)
- [Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items](https://mlsanity.com/paper/2106.11389/) (2021)
- [Diffusion-Based Data-Driven Assortment Optimization](https://mlsanity.com/paper/2608.11419/) (2026)
- [Logic-Logit: A Logic-Based Approach to Choice Modeling](https://mlsanity.com/paper/2610.05501/) (2026)

## Abstract (arXiv)

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we propose a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model -- a decision forest -- is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that with high probability, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose two practical algorithms -- one based on column generation and one based on random sampling -- for estimating such models from data. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms both rational and non-rational benchmark models in out-of-sample predictive ability.