Positive Political Theory I: Collective Preference. By David Austen-Smith and Jeffrey S. Banks. Ann Arbor: University of Michigan Press, 1999. 208p. $39.50

This study is intended as the first of a two-volume presenta- tion of positive political theory. As the authors indicate in the preface, in this volume they develop what may be termed Arrovian direct preference aggregation, a theory that exam- ines the properties of a direct aggregation rule, f, mapping from a domain of preference profiles on a set, X. For any profile, , the image of f is a social preference relation denoted f( ). The social relation may exhibit maximal or unbeaten outcomes, mf( ), in X itself. Thus, the volume is concerned with the "classification" of all social rules that map from preference profiles into X itself.