You cannot accurately estimate an individual’s loss aversion using an accept-reject task

Prospect theory’s loss aversion is often measured in the accept–reject task, in which participants accept or reject the chance of playing a series of gambles. The gambles are 2-branch 50/50 gambles with varying gain and loss amounts (e.g., 50% chance of winning $20 and a 50% chance of losing $10). Prospect theory quantifies loss aversion by scaling losses up by a parameter λ. Here, we show that λ suffers from extremely poor parameter recoverability in the accept–reject task. The λ cannot be reliably estimated even for a simple version of prospect theory with linear probability weighting and value functions. The λ cannot be reliably estimated even in impractically large experiments with participants subject to thousands of choices. The poor recoverability is driven by a tradeoff between λ and the other model parameters. However, a measure derived from these parameters is extremely well recovered—and corresponds to estimating the area of gain–loss space in which people accept gambles. This area is equivalent to the number of gambles accepted in a given choice set. That is, simply counting accept decisions is extremely reliably recovered—but using prospect theory to make further use of exactly which gambles were accepted and which were rejected does not work