Experimental Design Details
We implement a between-subject treatment design with three treatments, namely Treatment 1–Baseline, Treatment 2–GainFrame, and Treatment 3–LossFrame. In all treatments, subjects make a sequence of decisions and answer a questionnaire. The sequence includes two decisions in Treatment 1—Baseline, and three decisions in Treatments 2–GainFrame and 3–LossFrame.
The first decision (task T) in the three treatments is a choice between 14 Euro to be paid today and 17 Euro to be paid in five weeks.
The last decision in the three treatments is a choice between two lotteries (task R’). These two lotteries will be expressed in neutral terms, without emphasizing gains or losses. We adapt this task from a comparable one in Brown and Healy (EER, 2018). For example, the first lottery pays 18 Euro and 9 Euro, each with 50% probability. The second lottery pays 22 Euro with 75% probability, and 0 Euro with 25% probability.
The intermediate task that is only present in Treatments 2 and 3 but not in the baseline Treatment 1. This task is about making a choice between a safe payment and a lottery with loaded framing. We will use positive framing (emphasizing gains) in Treatment 2 and call it “task R+” and negative framing (emphasizing losses) in Treatment 3 and call it “task R-”. We adapt the two wording for the two frames directly from an experiment by De Martino et al. (Science, 2006).
For instance, each subject in Task R+ is endowed with 20 Euro and makes a choice between keeping 12 Euro for sure and a lottery with 75% probability of keeping all of the 20 Euro and 25% probability of keeping nothing. On the other hand, each subject in Task R- is endowed with 20 Euro and makes a choice between losing 8 Euro for sure and a lottery with 75% probability of losing nothing and 25% probability of losing all of the 20 Euro.
Summary of treatment design:
Treatment 1 (Baseline): First T, then R’.
Treatment 2 (Gain Frame): First T, then R+, then R’.
Treatment 3 (Loss Frame): First T, then R-, then R’.
A final questionnaire will include control variables such as measures of cognitive ability (Raven Matrices and Cognitive Reflection Test), trust, patience, engagement in risky behaviors, and socio-economic background.
For each subject, one of the choice-making tasks will be randomly selected to be paid. Payments will be made via bank transfers. This is communicated to the subjects in advance when sending the invitation emails.
Within the general research question whether the structure of projective measurements is a good description for the elicitation of individual preferences, we will focus on three specific questions of interest based on the experimental data. (1) Do we find statistical differences in the outcomes of the first task T? (2) Are there statistical differences between the fraction of subjects choosing the lottery in tasks R+/R- in treatments 2 and 3? (3) Do we find significant differences in the final task R’ across the three treatments? If so, can the projective model explain them as a result of the inclusion of the intermediate framed tasks R+ and R-? (4) Finally, can we conclude positively in favor of a model of projective measurement testing its goodness of fit? (This step is likely to require a simulation exercise).