When simulating robotic respondents’ answers to a CBC questionnaire, in order to recover known “true” utilities, one simulates the respondents answering the questionnaire according to known utilities but where the total utility of alternatives within each task is perturbed by independent Gumbel error. This is true to the logit rule and simulates the idea that respondents answer the calibration questionnaire with error.
When one wants to use the estimated utilities resulting from the choices to the CBC questionnaire to predict new holdout choices, one indeed could simulate discrete choices again using Gumbel error (applied to the total utility of concepts as estimated from the calibration questionnaire). But, to stabilize the probabilities of choices for holdout tasks at the individual level, one would need to simulate those choices with different draws of Gumbel error 1000s of times (and average the results at the individual level across the draws). However, we know that the expectation after millions of draws of Gumbel error of the probability of choices for holdout tasks for individuals converges to the logit rule. So, to shortcut the simulation procedure for holdout choices one can just use the logit rule as a closed form solution.
