A Bayesian method for measuring risk propensity in the Balloon Analogue Risk Task

The Balloon Analogue Risk Task (BART) is widely-used to measure risk propensity in theoretical, clinical, and applied research. In the task, people choose either to pump a balloon to increase its value at the risk of the balloon bursting and losing all value, or to bank the current value of the balloon. Risk propensity is most commonly measured as the average number of pumps on trials for which the balloon does not burst. Burst trials are excluded because they necessarily underestimate the number of pumps people intended to make. However, their exclusion discards relevant information about people's risk propensity. A better measure of risk propensity uses the statistical method of censoring to incorporate all of the trials. We develop a new Bayesian method, based on censoring, for measuring both risk propensity and behavioral consistency in the BART. Through applications to previous data we demonstrate how the method can be extended to consider the correlation of risk propensity with external measures, and to compare differences in risk propensity between groups. We provide implementations of all of these methods in R, MATLAB, and the GUI-based statistical software JASP.