# Pairwise Choice Markov Chains

arXiv: https://arxiv.org/abs/1603.02740 · HTML: https://mlsanity.com/paper/1603.02740/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2016.

## Built on by (most cited first, 10 of 10)

- [Algorithmic Monoculture and Social Welfare](https://mlsanity.com/paper/2101.05853/) (2021)
- [Learning Rich Rankings](https://mlsanity.com/paper/2312.15081/) (2023)
- [On Sinkhorn's Algorithm and Choice Modeling](https://mlsanity.com/paper/2310.00260/) (2023)
- [On the estimation of discrete choice models to capture irrational customer behaviors](https://mlsanity.com/paper/2109.03882/) (2021)
- [Exact and rapid linear clustering of networks with dynamic programming](https://mlsanity.com/paper/2301.10403/) (2023)
- [Choice Set Confounding in Discrete Choice](https://mlsanity.com/paper/2105.07959/) (2021)
- [Approximating a RUM from Distributions on k-Slates](https://mlsanity.com/paper/2305.13283/) (2023)
- [DeepHalo: A Neural Choice Model with Controllable Context Effects](https://mlsanity.com/paper/2601.04616/) (2026)
- [Consideration Circuits: Depth Separation and Universality Beyond a Single Softmax](https://mlsanity.com/paper/2610.04143/) (2026)
- [Similar Models, Broken Odds: Where Luce's Axiom Fails in Chatbot Arena](https://mlsanity.com/paper/2610.19095/) (2026)

## Abstract (arXiv)

As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansion, a considerably weaker assumption than Luce's choice axiom. We show that the PCMC model significantly outperforms the Multinomial Logit (MNL) model in prediction tasks on both synthetic and empirical datasets known to exhibit violations of Luce's axiom. Our analysis also synthesizes several recent observations connecting the Multinomial Logit model and Markov chains; the PCMC model retains the Multinomial Logit model as a special case.