Choices under risk often violate canonical axioms, like transitivity and stochastic dominance. These violations are in line with context-dependent theories, e.g. regret aversion, salience theory. These theories differ in whether they regard violations of these axioms as mistakes (e.g. due to blurred perception of probabilities) or true preference (e.g. regret avoidance). Moreover, existing evidence suggests that context-dependent theories have more explanatory power when the correlation structure is transparent. To investigate the effect of the transparency of the correlation structure on whether subjects regard their choices as mistakes and to dive deeper into the question whether violations of canonical axioms are mistakes or manifestations of preferences, we elicit preferences regarding axioms and lotteries building on the experimental paradigm by Nielsen and Rehbeck (2022). We classify those subjects who violate an axiom and, at the reconciliation stage, revise their lottery choices to comply with this axiom as subjects who make choice mistakes (and prefer to adhere to the axiom). Those subjects who violate an axiom and, at the reconciliation stage, choose to keep this violation and do not select the axiom are classified as subjects with a true preference for violating the axiom (violation is driven by “true” utility).
We find a systematic effect regarding the number of violations when switching from a transparent correlation structure to one that is opaque. However, contrary to previous studies, there does not seem to be a systematic effect between different display formats with precise (though not equally transparent) correlation structure. Compared to Nielsen and Rehbeck (2022), we find that in our data the support for the normative appeal of the canonical axioms is significantly weaker. This observation is based on two results: First, in our experiment axioms are selected significantly less often. Second, among those subjects who violate an axiom, significantly more prefer to keep the violation (and unselect the axiom) rather than to revise their lottery choice to be consistent with the axiom.