Experimental Design
The study consists of 34 tasks in total; 27 tasks each containing 33 choices that allow us to evaluate their equalizing reductions and an additional 7 certainty equivalent tasks each consisting of 26 choices to evaluate parameters of their utility functions and probability weighting functions.
The first 27 tasks consist of choices between two binary lotteries, referred to as Option A and Option B, each consisting of three outcomes with positive probability. Option A remains the same throughout all of the choices in the task, while the third outcome for Option B decreases by increments of 50 cents, allowing us to pin down the participant's equalizing reduction, k. Nine values of X (2, 3, 4, 21, 22, 23, 30, 31, 32) each for three different probability vectors {p, q, 1-p-q} = {20, 60, 20}, {40, 20, 40}, and {40, 30, 30} give us the 27 total tasks.
In the next seven tasks, participants complete a set of similar choices, where instead, Option A is a lottery between two outcomes: $24 and $-1 for the gain condition, $5 and $-20 for the gains and losses condition, and $-15 and $-40 for the loss condition. We discuss these three conditions in the following section. Option B is a certain amount of money, starting with greatest outcome in Option A and dropping by 50 cents for each following choice within the task. We ask participants to complete this task for seven different probability vectors for the two outcomes in Option A. We include {p, 1-p} = {95, 5}, {90, 10}, {75, 25}, {50, 50}, {25, 75}, {10, 90}, and {5, 95}. Through this set of tasks, we are able to identify participants' parameters on their utility function and probability weighting functions, using Kahneman and Tversky's (1992) functional forms. Using the imputed parameters, we can predict how much the change in the rank of X should affect certainty equivalents according to CPT.
The experiment will be run using oTree, an online survey interface. It integrates a point and click interface called oTree Studio with Django, HTML, and Python. See the appendix in the Analysis Plan for screenshots of the study for participants in the gain condition. After completing the equalizing reductions and certainty equivalents tasks, participants finish the study by answering a short post-study survey containing demographic questions, logic questions, and questions on their perceptions of hypothetical lotteries.
We will recruit 150 undergraduate students at UC San Diego to the economics lab. Participants will be randomized into one of three groups. Each group will receive a different amount of money in an envelope upon entry to the experimental lab: $1, $20, or $40. They are told that the money inside the envelope is their own money. We treat the money in the envelope as the subject's reference point. Once the participant opens the envelope, we have no degrees of freedom on this parameter.