It has been more than thirty-five years since the publication of Downs's (1957) seminal volume on elections and spatial theory and more than forty since Black and Newing (1951) offered their analysis of majority rule and committees. Thus, in response to the question “What have we accomplished since then?” it is not unreasonable to suppose that the appropriate answer would be “a great deal.” Unfortunately, reality admits of only a more ambiguous response.

It is true that developments in the spatial analysis of committees and elections has covered considerable ground since 1957. Beginning with Davis and Hinich's (1966) introduction of the mathematics of Euclidean preferences, Plott's (1967) treatment of contract curves and symmetry, and Kramer's (1972) adaptation of Farquharson's (1969) analysis of strategic voting in committees with spatial preferences, many of Downs's and Black and Newing's ideas have been made rigorous and general. The idea of spatial preferences - of representing the set of feasible alternatives as a subset of a ra-dimensional Euclidean space, of labeling the dimensions “issues,” of assuming that people (legislators or voters) have an ideal preference on each issue, and of supposing that each person's preference (utility) decreases as we move away from his or her m dimensional ideal policy - is now commonplace and broadly accepted as a legitimate basis for modeling electorates and parliaments. Moreover, since Weisbergh and Rusk's (1970) initial application of multidimensional scaling, considerable advances have been made in developing statistical methodologies for measuring those preferences within electorates (see, for example, Aldrich and McKelvey 1977; Enelow and Hinich 1982; Poole and Rosenthal 1984; Chu, Hinich, and Lin 1993) and legislatures (Poole and Rosenthal 1985, 1991; Hoadley 1986).