Table 2: Total variation error in percentage points, for simulated data sets with 12 choice items. See the caption accompanying Table 1. Figure 1: Triangle plot of the true predictive choice distribution and its estimates in the three-item case, for the simulation with 250 decision-makers, 10 attributes, and high het- erogeneity. See accompanying text. 15 0 0.4 Item 1 0.3 0.6 Item 2 0.9 0.1 Item 3 true veb vbayes mean mcmc mean vbayes density mcmc density 3 attributes 10 attributes Agents Het. VEB VB MCMC VEB VB MCMC 250 Low 2.88 2.80 2.64 1.97 1.91 2.44 High 1.44 1.94 1.64 2.43 2.37 2.62 1,000 Low 1.11 1.27 1.09 0.99 1.00 1.60 High 0.98 1.18 1.18 1.99 2.05 1.96 5,000 Low 1.25 1.45 1.18 0.95 1.13 0.97 High 1.14 0.98 1.10 0.71 0.91 0.92 25,000 Low 0.22 0.33 NA 0.51 0.53 NA High 0.99 0.57 NA 1.23 0.96 NA