Individual differences in the algebraic structure of preferences

Two divergent theories regarding the algebraic structure of preferences are the strict weak-order (i.e., utility) representation, and the lexicographic semiorder representation. We carry out a novel comparison of these theories by formulating them as mixture models of ternary choice that are general yet parsimonious. We apply Bayesian model selection to see which representation (if any) best explains each decision maker's choices across multiple data sets. We report the results of a new experiment, which tests the robustness of each representation with respect to manipulations of stimuli, display format, and time pressure. We find that a majority of participants are best described by strict weak-ordered preferences with a substantial minority best described by lexicographically semi-ordered preferences.