Salience theory (Bordalo et al., 2012) predicts that choices between two lotteries are driven not only by the marginal distributions of the lotteries, but also by the correlation between the two lotteries. Existing studies testing this prediction fail to control for event-splitting effects. In this paper, we seek to disentangle the role of correlation and event-splitting in two settings: 1) choices between Mao pairs as studied by Dertwinkel-Kalt and Köster (2019); 2) the Allais paradox. We further test for correlation effects in a novel task in which subjects have to choose between two lotteries with the same marginal distribution. This task allows to detect correlation effects even when they are of second-order importance only.
We run a lab experiment. Participants make multiple choices between two lotteries and answer a survey. One of the lottery choices is randomly selected, and participants are paid on the basis of this choice. We study whether lottery choices are impacted by the correlation of the lotteries.
For a detailed description of the experimental design and the lotteries we employ, see the document "Experiment_description".
Our study consists of five parts. In Part I, participants face 6 pairs of Mao-lotteries, each in maximally positive and maximally negative correlation structure. In Part II, participants face 3 lottery pairs that might elicit the common consequence Allais paradox. Participants face lotteries both when they are maximally positively correlated and when they are independent. In part III, subjects face 2 lottery pairs for which one lottery dominates the other. Subjects see these lotteries both in a maximally positive correlation and in a maximally negative correlation structure. In part IV, participants decide between two lotteries with the same marginal distribution, but different relative skewness. In part V, Subjects also decide between two lotteries with the same marginal distribution, but different relative skewness. However, they now receive immediate feedback on the outcome of their decisions.
There are two treatments. In the treatment correlation effects and event splitting effects (CEESE), changing the correlation structure for part I and II also induces changes in the way events are split and in the number of events. In the treatment correlation effects only (CEO), event splitting effects are controlled for. For the parts III-V, there is no difference between the treatments.
Intervention Start Date
2021-03-08
Intervention End Date
2021-03-19
Primary Outcomes (end points)
For decisions in parts I-III: Choice reversals due to changes in the correlation structure (and event-splitting). For decisions in part II: Choice reversals due the common consequence.
For decisions in parts IV and V: Frequency of choices of the lottery with a higher relative skewness.
Primary Outcomes (explanation)
For more details on the variable construction, see the analysis plan.
Secondary Outcomes (end points)
Secondary Outcomes (explanation)
Experimental Design
For a detailed description of the experimental design, see the document "Experiment_description.pdf".
Experimental Design Details
Randomization Method
By Computer.
Randomization Unit
Individual.
Was the treatment clustered?
Yes
Sample size: planned number of clusters
150 individuals for each of the two treatments.
Sample size: planned number of observations
35 decisions for each of the 300 participants. For part I: 6 paired choices per participant. For part II: 3 paired choices per participant. For part III: 2 paired choices per participant. For part IV and V: 5 choices each per participant.
Sample size (or number of clusters) by treatment arms
For part I and II: 150 participants in each treatment. For each participants there are 6 (part I), and 3 (part II) paired choices. For part III-V, there is no difference by treatment.
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)