Expected attenuation of the correlation between the δ parameters of cumulative prospect theory. We conducted five sets of simulations, each with a different value of the true correlation. For each set, we generated 1,000 synthetic data sets. The gray violin plots show the distribution of the 1,000 Pearson correlation coefficients r* for the five values of the true correlation. The r* values were generated using the estimation uncertainties $σϵδ1$ and $σϵδ2$ and the posterior means of the group-level µ_δ1, µ_δ2, $σδ12$⁠, and $σδ22$ parameters obtained from the Glöckner and Pachur (2012) data. The upper arrow shows the posterior mean of the inferred correlation ρ in the observed data. The lower arrow shows the Pearson correlation coefficient r between the point estimates $δ^1$ and $δ^2$ in the observed data. The figure shows that (1) the attenuation increases with the absolute value of the true correlation, and (2) the observed Pearson r between the point estimates is well within the 2.5^th and 97.5^th percentile of the r* values predicted by the simulations.