The Euclidean representation of political issues and alternative outcomes, and the associated representation of preferences as quasiconcave utility functions, is by now a staple of formal models of committees and elections. This theoretical development, moreover, is accompanied by a considerable body of experimental research. We can view that research in two ways: as a test of the basic propositions about equilibria in specific institutional settings, and as an attempt to gain insights into those aspects of political processes that are poorly understood or imperfectly modeled, such as the robustness of theoretical results with respect to procedural details and bargaining environments. This essay reviews that research so that we can gain some sense of its overall import. A considerable body of political theory represents alternative outcomes or policies by a subset of n-dimensional Euclidean space, and assumes that we can represent individual preferences over these outcomes by quasiconcave utility functions with internal satiation points. By imposing this particular structure on alternatives and preferences, we can deduce a variety of substantively informative results, such as the Median Voter Theorem in elections, and the generic emptiness of cores in cooperative political games (cf. Plott 1967, Schofield 1983). Correspondingly, the special case of Euclidean preferences, introduced by Davis and Hinich (1966, 1968), form the basis for the most extensively developed models of two general classes of political institutions – elections and committees.
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