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 in 1977, who models the choice probability 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 (CMNL), uses explicit alternative elimination. It is easier to implement but can only be understood as an approximation of Manski's approach. We analyze in which situations this approximation is appropriate by estimating models with both approaches over synthetic data and comparing the results.