Three experiments tested if individuals show violations of transitivity in choices between risky gambles in linked designs. The binary gambles varied in the probability to win the higher (better) prize, the value of the higher prize, and the value of the lower prize. Each design varied two factors, with the third fixed. Designs are linked by using the same values in different designs. Linked designs allow one to determine if a lexicographic semiorder model can describe violations of transitivity in more than one design using the same parameters. In addition, two experiments tested interactive independence, a critical property implied by all lexicographic semiorder models. Very few people showed systematic violations of transitivity; only one person out of 136 showed violations of transitivity in two designs that could be linked by a lexicographic semiorder. However, that person violated interactive independence, as did the majority of other participants. Most individuals showed systematic violations of the assumptions of stochastic independence and stationarity of choice responses. That means that investigators should evaluate models with respect to response patterns (response combinations) rather than focusing entirely on choice proportions.