Primary Outcomes (explanation)
1. Each implementer faces two simple menus that are each repeated twice and faces two complex menus that are each repeated twice. For each repeated menu, we create an indicator equal to "1" if the implementer chose a different lottery across repeats, 0 otherwise. We call these inconsistent guesses "noise." We compare the aggregate rates of noise between the simple lotteries and the complex lotteries.
2. We conduct a similar analysis at the individual level. For each implementer, we can say whether they were noisier in the complex menus, noisier in the simple menus, or equally noisy. We test whether implementers were noisier in the complex vs. simple menus.
3. We use our measures of procedural decision-making (e.g., whether a message is "perfectly replicable") developed earlier to test whether procedures are less noisy than non-procedures. These measures of procedural decision-making were created in our earlier study.
4. Restricting to the set of comparable lotteries with 10 outcomes, we test whether simple or complex messages lead to more noise and whether procedures interact with this effect.
5. We test whether implementers violate FOSD more for simple or complex lotteries (both at the individual level and in aggregate). We also test whether procedures interact with this effect.
Given potential data quality concerns on Prolific, we will investigate the sensitivity of our results to indicators of low data quality. In particular, we will investigate the sensitivity of our results to removing individuals with very fast survey completion times relative to others, and those with higher comprehension question errors relative to others.