Markov Stochastic Choice

TL;DR

This paper introduces a Markovian decision-making model based on stochastic pairwise comparisons, analyzing how item arrangement influences choices and identifying conditions under which choices are unaffected by such arrangements.

Contribution

It provides a novel Markovian framework for modeling stochastic choice, characterizes reversible and all-pair comparison models, and links these to the Luce model, enhancing understanding of decision processes.

Findings

Reversible Markov models are unaffected by item rearrangements.

Models allowing all pairwise comparisons are observationally equivalent to the Luce model.

Choice data can reveal consideration sets and the impact of initial fixation.

Abstract

We examine the effect of item arrangement on choices using a novel decision-making model based on the Markovian exploration of choice sets. This model is inspired by experimental evidence suggesting that the decision-making process involves sequential search through rapid stochastic pairwise comparisons. Our findings show that decision-makers following a reversible process are unaffected by item rearrangements, and further demonstrate that this property can be inferred from their choice behavior. Additionally, we provide a characterization of the class of Markovian models in which the agent makes all possible pairwise comparisons with positive probability. The intersection of reversible models and those allowing all pairwise comparisons is observationally equivalent to the well-known Luce model. Finally, we characterize the class of Markovian models for which the initial fixation does not impact the final choice and show that choice data reveals the existence and composition of consideration sets.