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

A classic paper by Tversky (Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31–48.) reported that some people systematically violated transitivity of preference when choosing between specially constructed risky gambles. This conclusion remained controversial because his statistical analysis did not allow each participant to have a different true preference order. Recently, however, it has been argued that an inherently intransitive process governs risky decision making. This paper uses a relatively new statistical technique for testing transitivity and analyzes two new experiments in which hundreds of participants made choices among the same gambles studied by Tversky. It was found that very few people repeated intransitive patterns. The incidence of violation of transitivity was slightly higher when probability was displayed graphically without numerical information, but even in this condition few participants were intransitive. Furthermore, even among those few who appeared to be intransitive, most showed dimension interaction, contrary to implications of the lexicographic semi-order. These results cast doubt on a lexicographic semi-order as a descriptive theory of risky decision making.