In this paper, we compare two methods to model the formation of choice sets in the context of discrete choice models. The first method is the probabilistic approach proposed by Manski (1977), who explicitly models the choice set generation process by expressing the choice as the joint probability of selecting a choice set and an alternative from this set. This approach is theoretically sound and unbiased, but it is hard to implement due to the complexity that arises from the combinatorial number of possible choice sets. The second method, known as the Constrained Multinomial Logit (Martinez et al., 2009), models the choice set generation process implicitly through elimination of alternatives. This approach is easier to implement because it does not require to enumerate the possible choice sets, allowing to deal with large choice sets, but can only be understood as an approximation of Manskis approach. An experimental analysis and comparison of both methods in presented. Results based on synthetic data show that the Constrained Multinomial Logit may be a poor approximation of Manskis model, with some clear exceptions which are identified and analyzed.