The Dependence of Classic and Dual Common Consequence Effects on the Choice-set Outcome Range: From the Perspective of Probability Weights

Abstract: Expected utility theory (EUT) was considered capable of aptly explaining individual choice behavior. However, a plethora of research has uncovered phenomena that violate EUT, such as the classic common consequence effect (CCCE) and the dual common consequence effect (DCCE), especially when the choice-set outcome range (COR) is broad. Subsequent scholars have examined the stability of behaviors that violate EUT by conducting empirical studies within a narrow COR. They discovered that CCCE no longer appeared, thereby suggesting that individuals’ behaviors conform to EUT under these conditions. Nevertheless, the absence of CCCE does not imply the nonexistence of DCCE. Studies on CCCE with a narrow COR typically employ a specific probability level without exploring whether the effect remains absent under other probability levels. Given these considerations, this study sequentially addresses three questions: first, whether DCCE exists within a narrow COR and how changes in COR influence this effect; second, whether the impact of COR on CCCE is also stably present at other probability levels; and third, what the underlying mechanisms are if changes in COR influence both types of common consequence effects.
This study conducted two experiments to address the aforementioned questions. In Experiment 1, a choice task was executed to explore whether the COR affects both types of common consequence effects. This experiment employed a between-subjects design with two experimental groups: the broad-range group and the narrow-range group. A total of 160 participants were recruited for the experiment and were randomly and equally distributed into the two groups. Given that 10 participants failed the attention check, the effective sample sizes were 74 and 76 for the two groups, respectively. The experimental materials for both groups were consistent in terms of probability values. Meanwhile, the outcome values for the broad-range group were 100 times those of the narrow-range group. The Conlisk-z test method was utilized to analyze the occurrence of CCCE and DCCE. Furthermore, the Wilcoxon signed-rank test was employed to examine the impact of COR on these effects. In Experiment 2, a nonparametric approach was used to explore the mechanisms by which the COR influences CCCE and DCCE from the perspective of probability weights. The experiment adopted a within-subject design, which was conducted in two phases: broad- and narrow-range phases. A total of 55 participants were invited to partake in the experiment. The t-test was utilized to analyze the influences of COR on probability weights.
The results of Experiment 1 indicate that DCCE not only exists within a narrow COR but also occurs more readily than a broad COR. Compared with a broad COR, CCCE significantly reduced, but persists in a narrow COR. The results of Experiment 2 demonstrate that the outcome range of choice sets influences both types of common consequence effects by altering individuals’ risk perception of objective probabilities (i.e., probability weights). The impact of COR on probability weights manifests such that a narrower COR entails a higher probability weight assigned by decision-makers to favorable outcomes.
Our research contributes to the literature in four ways. First, this study addresses the lack of generality in the experimental materials of existing related research by employing various levels of probabilities to investigate CCCE empirically. Second, the identification of DCCE within narrow COR challenges the viability of EUT in such contexts. Third, this research clarifies the mechanisms through which COR influences CCCE and DCCE from the perspective of probability weights. Hence, this work not only offers a new perspective for explaining the relationship between decision-making behaviors and COR but also provides empirical evidence for the development of non-EUT theories, such as cumulative prospect theory (CPT). Last, the improvements made to the existing trade-off method not only offer an operable experimental scheme for verifying the dependency relationship between probability weights and COR but also pave the way for the application of COR-dependent CPT. Beyond the theoretical contributions outlined above, our study provides practical insights for blind box sales. For instance, reducing the packaging of products is beneficial for increasing sales.