Hannes Malmberg: Random Choice over a Continuous Set of Options

Random choice theory has traditionally modeled choices over a finite number of options. This thesis generalizes the literature by studying the limiting behavior of choice models as the number of options approaches a continuum. The thesis uses the theory of random fields, extreme value theory and point processes to calculate this limiting behavior. For a number of distributional assumptions, we can give analytic expressions for the limiting probability distribution of the characteristics of the best choice. In addition, we also outline a straightforward extension to our theory which would significantly relax the distributional assumptions needed to derive analytical results. Some examples from commuting research are discussed to illustrate potential applications of the theory.