Testing for intransitivity of preferences predicted by a lexicographic semi-order

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Transitive in Our Preferences, But Transitive in Different Ways: An Analysis of Choice Variability (2014, methodology): “There are other promising approaches to modeling stochastic choice that are capable of capturing such additional structure in the data, such as the “true and error” approach of Birnbaum and Gutierrez (2007).”
An experimental investigation of violations of transitivity in choice under uncertainty (2008, methodology): “The success of transitivity in our data is compatible with findings of Birnbaum and Gutierrez (2007), who tested violations of transitivity predicted by a lexicographic semi-order, as previously studied by Tversky (1969).”