Revealed preference domains from random choice

Ordinal random utility models (RUMs) are based on the presumption that fluctuating preferences drive stochastic choices. We study a novel property of RUM subclasses called exclusiveness, satisfied whenever the supports of all RUM representations of stochastic choice data, rationalizable by a RUM over preferences within a specific domain, also belong to that domain. We demonstrate that well-known preference domains such as the single-peaked, single-dipped, triple-wise value-restricted and peak-monotone are RUM-exclusive, alongside a novel domain we term peak-pit on a line. Building on existing characterization results, we show how these preference domains can be directly revealed from stochastic choice data, without the need to compute all RUM representations.