Pairwise Choice Markov Chains
This work addresses the need for more flexible choice models in online domains where human choices often break traditional assumptions, offering an inferentially tractable alternative that retains MNL as a special case.
The authors tackled the problem of modeling human choices in rich datasets that violate traditional axioms like Luce's choice axiom, by introducing the Pairwise Choice Markov Chain (PCMC) model, which significantly outperforms the Multinomial Logit (MNL) model in prediction tasks on synthetic and empirical datasets.
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.