Discrete choice models are defined conditional to the analyst's knowledge of the actual choice set. The common practice for many years has been to assume that individual-based choice sets can be deterministically generated on the basis of the choice context and characteristics of the decision maker. This assumption is not valid or not applicable in many situations, and probabilistic choice set formation procedures must be considered. The constrained multinomial logit model (CMNL) has recently been proposed as a convenient way to deal with this issue, as it is also appropriate for models with a large choice set. In this paper, how well the implicit choice set generation of the CMNL approximates the explicit choice set generation is analyzed as described in earlier research. The results based on synthetic data show that the implicit choice set generation model may be a poor approximation of the explicit model.