Transitive preference, i.e., if you prefer apples to bananas and bananas to cherries, you also prefer apples to cherries, is a basic property of some influential rational choice models. Contrary to this, Tversky, in his seminal 1969 article, presented evidence of intransitive preferences in two contexts, one of which involved choices between simple monetary lotteries. Whilst early replications corroborated his findings, more recent research cast doubt on the strength of evidence of intransitive preferences in this task. Here, from Tversky’s extended additive difference model we develop a simplified additive difference (SAD) model which corresponds to alternative dimensional processing strategies. This predicts transitive or intransitive preferences, depending on its parameter values. We review six replications of Tversky’s lottery task and fit variants of the model to the choice data. We estimate the SAD model’s parameters for each individual data set using maximum likelihood estimation, examine the goodness of fit of the model and use likelihood ratio tests to evaluate specific variants. The model has a very good fit to most individual choice data sets reviewed, with many predictably violating weak stochastic transitivity. We also find that many transitive patterns correspond to the application of simple, one-dimensional ‘take the best’ heuristics. The findings support the view that human decision making is often based on dimensional processing in such a way that evaluations of decision alternatives are relative to the set under consideration, resulting in intransitivity of preferences.
Ranyard, R., Montgomery, H., Konstantinidis, E., & Taylor, A. L. (in press). Intransitivity and Transitivity of Preferences: Dimensional Processing in Decision Making. Decision. http://eprints.whiterose.ac.uk/162973/3/Intransitivity%20and%20Transitivity%20Final%20June%2030%202020.pdf