As choice modelers we observe decision makers’ choices among competing alternatives, and we try to come up with a model that best describes the observed choice behavior. The economic model of the rational utility maximizer is still pervasive. This model of behavior is based on the assumption that a decision maker has complete information about all products in a market and full knowledge of their preferences. The chosen alternative is then the one that gives the highest utility. In the real world, it is rare that people have complete information about all available alternatives, i.e. people do not have a fully formed set of alternatives (choice set) from which they can choose. Instead, people need to search for information about new alternatives. This implies that a decision maker’s consideration set is growing with one alternative per period of search. Optimal search theory stipulates that this search process will continue as long as the expected gain from continuing to search exceeds the cost of doing so. At the point where search stops, a choice is made among the alternatives in the consideration set. Note that this consideration set is a proper subset of the complete choice set. However, current choice models, using both revealed and stated preference data, all but ignore the choice set generation process, which is characterized by the sequential and ordered search process. That said, there are several papers out there assuming some form of choice set generation process, however, we argue that these approaches are missing the mark by ignoring the search process. The search process is driven by the expectation that there might be a better alternative out there, i.e. a decision maker will continue to search as long as the expected utility of the unseen alternatives is higher than the current highest utility plus search costs. Not only will failing to consider the search process ignore an important source of heterogeneity, which arises because different decision makers considered different alternatives in different orders, but it runs the risk of underestimating the probabilities of choice. Interestingly, a decision made among alternatives in a consideration set generated in this manner, is a decision made with incomlete information. If the choice among alternatives is made in a utility maximizing manner, then the choice may only be a local, as opposed to a global, maximum.
To illustrate how our model works, assume that you are in the market for shoes. It is unlikely that you have complete information about all pairs of shoes out there and full knowledge of your preferences for each of those pairs. Instead, you start searching. You go to a store and you look at a pair of shoes (your first alternative). Assuming that you have no other information about shoes, you do not know whether this is a ``good” pair of shoes. The question is: what is the probability that another pair of shoes that you have not yet seen gives higher utility than the pair you have seen plus the cost of searching for another alternative? If the answer is sufficiently large, you look at another pair of shoes, i.e. you grow your consideration set by revealing another alternative. As you establish more information on shoes you are better able to determine the probability that there is a better pair of shoes out there. In other words, as you learn about new alternatives you learn about your preferences and you update your search probability. When the search probability becomes suffiently small you stop search and make a choice among the shoes in your consideration set. Note that this process implies that your consideration set might not contain the global utility maximizing choice and that you might continue searching after you have encountered your utility maximizing choice if your expectaions about what other options exist are unrealistically high. Importantly, it allows the analyst to determine a smaller possibly more correct consideration set.
In this paper we develop a novel model that explicitly considers the information search process and the role it plays in choice set generation. For convenience, we let the choice among alternatives in the consideration set be described by a utility maximization rule. We test our model on equally novel data collected through a sequential search process, where at each stage, the decision maker has to choose whether to reveal another alternative or make a choice among the ones she has already seen. We show through Monte-Carlo simulations that our model is able to retrieve consistent parameter estimates and correctly predict decision makers’ choices conditional on their consideration set. We run simulations under various assumptions with respect to the parameters, number of alternatives and sample sizes. We then compare our model’s ability to retrieve consistent estimates against more standard discrete choice models. Finally, we show how our model performs on real data gathered in a conventional way and gathered using a sequential approach. The sequential approach more closely mirrors real life behavior and our model is developed specifically to address this.