Individual differences in the algebraic structure of preferences

• Published in: Journal of mathematical psychology Vol. 66; pp. 70 - 82
• Main Authors: Davis-Stober, Clintin P., Brown, Nicholas, Cavagnaro, Daniel R.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.06.2015
• Subjects: Choice modeling; Convex polytopes; Lexicographic semiorders; Order-constrained inference; Preferential choice; Random preference; Weak orders; Lexicographic semiorders; Convex polytopes; Random preference; Weak orders; Preferential choice; Order-constrained inference; Choice modeling
• ISSN: 0022-2496; 1096-0880
• DOI: 10.1016/j.jmp.2014.12.003

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. •We examine the algebraic structure of individual preference.•We evaluate a large class of weak-order and lexicographic semiorder based theories.•We present a new study as well as a re-analysis of an existing data set.•We find that a majority of subjects’ preferences are consistent with weak orders.•We find that the remaining subjects are well-described by lexicographic semiorders.