Discrete choice models are defined conditional to the knowledge of the actual choice set by the analyst. The common practice for is to assume that individual-based choice sets can be deterministically generated based on the choice context and the characteristics of the decision maker. There are many situations where this assumption is not valid or not applicable, and probabilistic choice set formation procedures must be considered. The Constrained Multinomial Logit model (CMNL) has recently been proposed by Martinez et al. (2009) as a convenient way to deal with this issue, as it is also appropriate for models with a large choice set. In this paper, we analyze how the implicit choice set generation of the CMNL compares to the explicit choice set generation as described by Manski (1977). The results based on synthetic data show that the implicit choice set generation model may be a poor approximation of the explicit model. (joint work with Ricardo Hurtubia and Gunnar Flötteröd)