Testing lexicographic semiorders as models of decision making: Priority dominance, integration, interaction, and transitivity

Three new properties are devised to test a family of lexicographic semiorder models of risky decision making. Lexicographic semiorder models imply priority dominance, the principle that when an attribute with priority determines a choice, no variation of other attributes can overcome that preference. Attribute integration tests whether two changes in attributes that are too small, individually, to be decisive can combine to reverse a preference. Attribute interaction tests whether preference due to a given contrast can be reversed by changing an attribute that is the same in both alternatives. These three properties, combined with the property of transitivity, allow us to compare four classes of models. Four new studies show that priority dominance is systematically violated, that most people integrate attributes, and that most people show interactions between probability and consequences. In addition, very few people show the pattern of intransitivity predicted by the priority heuristic, which is a variant of a lexicographic semiorder model with additional features chosen to reproduce certain previous data. When individual data are analyzed in these three new tests, it is found that few people exhibit data compatible with any of the lexicographic semiorder models. The most frequent patterns of individual data are those implied by Birnbaum's transfer of attention model with parameters used in previous research. These results show that the family of lexicographic semiorders is not a good description of how people make risky decisions.