Acceptance of Mixed Gambles Is Sensitive to the Range of Gains and Losses Experienced, and Estimates of Lambda (λ) Are Not a Reliable Measure of Loss Aversion: Reply to André and de Langhe (2020)

Walasek and Stewart (2015) demonstrated that loss aversion estimated from fitting accept–reject choice data from a set of 50–50 gambles can be made to disappear or even reverse by manipulating the range of gains and losses experienced in different conditions. André and de Langhe (2020) critique this conclusion because in estimating loss aversion on different choice sets, Walasek and Stewart (2015) have violated measurement invariance. They show, and we agree, that when loss aversion is estimated on the choices common to all conditions, there is no difference in prospect theory’s λ parameter. But there are two problems here. First, while there are no differences in λs across conditions, there are very large differences in the proportion of the common gambles that are accepted, which André and de Langhe chose not to report. These choice proportion differences are consistent with decision by sampling (but are inconsistent with prospect theory or any of the alternative mechanisms proposed by André & de Langhe, 2020). Second, we demonstrate a much more general problem related to the issue of measurement invariance: that λ estimated from the accept–reject choices is extremely unreliable and does not generalize even across random splits within large, balanced choice sets. It is therefore not possible to determine whether differences in choice proportions are due to loss aversion or to a bias in accepting or rejecting mixed gambles. We conclude that context has large effects on the acceptance of mixed gambles and that it is futile to estimate λ from accept–reject choices.