Testing transitivity of preference in individuals.

Abstract

This experiment tested transitivity of preferences in individuals using the stimulus design of Butler and Pogrebna (2018). That design was constructed to find violations of transitivity that would occur if people chose the alternative with a higher probability of yielding better outcomes. Each choice problem was presented 60 times (replicated twice in each of 30 sessions). The individual true and error (TE) model was used to estimate incidence of transitive and intransitive preference patterns and error rates for each choice problem for each person. Although the data of most participants were consistent with transitivity, 7 of 22 participants showed significant evidence of intransitive preferences patterns at least part of the time, and 14 participants showed evidence of changing true preferences over time. Systematic violations of the assumption that responses are independently and identically distributed (iid) were observed. Although TE models assume errors are mutually independent, they do not imply that responses will satisfy iid; instead, responses will violate independence when there is a mixture of preference patterns. Markov true and error (MARTER) models in which parameters can change gradually over sessions imply positive correlations between the frequency of preference reversals and the gaps between sessions. Positive correlations were observed for 21 of 22 participants; these were significant for all but 7, 4 of whom were compatible with a single true preference pattern throughout the study. Advantages of TE models (which can analyze response patterns and choice proportions) over older approaches (which analyze only binary choice proportions) are discussed.

Addiction and Rational Choice: Evidence from an Eye Tracking Experiment with Cigarette Packages

“…For example, if we regard higher utility as meaning less risky, we can represent the smoker's preferences in this case by a utility function with values 𝑢(𝑥) = 3, 𝑢(𝑥´) = 2 and 𝑢(𝑥´´) = 1. Violations of transitivity result in preference cycles, which have repeatedly been observed in some but not all experimental settings (Birnbaum & Bahra, 2012;Birnbaum et al, 2016;Tversky, 1969). 𝑢 " (𝑏) > 𝑢 !…”

True and error analysis instead of test of correlated proportions: Can we save lexicographic semiorder models with error theory?

“…In contrast, TE methods correctly diagnose which type of model was used to simulate the data. TE methods for analysis of the issue of transitivity have been presented in Birnbaum & Bahra (2012b), Birnbaum & Wan (2020), Schramm (2020), and Birnbaum (2022).…”

“…Indeed, Tversky (1969) concluded that only a small proportion of the people tested showed evidence of the intransitive behavior that could be described by his LS model. Other studies also found that only a fraction of participants shows the predicted intransitive behavior (Ranyard et al, 2020;Birnbaum & Gutierrez, 2007;Birnbaum & Bahra, 2012b;Birnbaum, 2010Birnbaum, , 2020Birnbaum, , 2022Butler & Pogrebna, 2018).…”

“…A rival method to TE models for the analysis of response proportions in within-subject studies is the Qtest approach, described in Regenwetter et al (2014) and updated in Zwilling et al (2019). This approach has been applied to cases of individual data with the assumption that repeated responses by the same person are independent and identically distributed (iid); however, that iid assumption has been found to be systematically violated in empirical choice data obtained from individuals (Birnbaum, 2012(Birnbaum, , 2013(Birnbaum, , 2022Birnbaum & Bahra, 2012a, 2012b, including reanalysis of the data of Regenwetter et al (2011).…”

Dominance and transitivity

“…These 4 triples were later tested in a new study with 22 individuals who responded 60 times to each choice problem (Birnbaum, 2023a), which allowed analysis via the individual TE model. Birnbaum (2023a) concluded that although most individuals satisfied transitivity, 1 person showed violations consistent with the MPW model, and 6 others showed evidence of intransitive behaviors in at least one of the triples at least part of the time.…”