Preseparable Extensions of Multidimensional Preferences

Throughout much of the literature in economics and political science, the notion of separability provides a mechanism for characterizing interdependence within individual preferences over multiple dimensions. In this paper, we show how preseparable extensions can be used to construct certain classes of separable and non-separable preferences. We prove several associated combinatorial results, and we note a correspondence between separable preference orders, Boolean term orders, and comparative probability relations. We also mention several open questions pertaining to preseparable extensions and separable preferences. This work was partially supported by National Science Foundation grant DMS-0451254, which funds a Research Experience for Undergraduates program at Grand Valley State University. Portions of this paper are adapted from Hodge’s doctoral dissertation 4]. The authors wish to thank the referees and editor for their helpful comments and suggestions.