A Model-Agnostic Laplacian Criterion for Assortment Experiment Design

Firms learn choice models by offering assortments and recording choices; which assortments to offer is an experiment design problem. Classical Bayesian criteria are model- and prior-dependent, and therefore do not provide a common design ranking before those choices are fixed. We propose selecting designs by the spectrum of the design Laplacian, a purely combinatorial object. Inspired by MNL, we prove that for item-indexed, shift-invariant choice models under any exchangeable prior, the prior-averaged Fisher information is a scalar multiple of the Laplacian, so the design can be fixed before the model is chosen; we also prove this exactness fails for more complicated classes, e.g.\ for the Markov chain model. Numerically the criterion works beyond its guarantee: the $\lambda_2$-maximizing design reduces estimation error by $8$--$24$% under MNL, Markov chain, and ranked-list ground truths, including under misspecification.