On the Relation Between Several Discrete Choice Models

In this paper, we study the relation between several well known classes of discrete choice models, namely the random utility model (RUM), the representative agent model (RAM) and the semi-parametric choice model (SCM). Using a welfare based model as an intermediate, we show that the RAM and the SCM are equivalent. Furthermore, we show that both models as well as the welfare based model strictly subsume the random utility model when there are three or more alternatives, while the four are equivalent when there are only two alternatives. Thus, this paper presents a complete picture on the relation between these choice models