Pairwise Choice Markov Chains

TL;DR

This paper introduces the Pairwise Choice Markov Chain (PCMC) model, a flexible discrete choice model that relaxes traditional axioms and outperforms the Multinomial Logit in predicting human choices, especially when axioms are violated.

Contribution

The PCMC model is a novel, tractable choice model that does not rely on traditional axioms like Luce's, and it generalizes the Multinomial Logit model.

Findings

PCMC outperforms MNL in prediction accuracy on synthetic datasets.

PCMC remains effective when choice axioms are violated.

PCMC includes MNL as a special case.

Abstract

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.