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Spatial characterizations of agents’ preferences lie at the heart of many theories of political competition. These give rise to explicitly dimensional interpretations. Parties define and differentiate themselves in terms of substantive policy issues, and the configuration of such issues that is required for a good description of political competition affects how we think substantively about the underlying political space in which parties compete. For this reason a great deal of activity in political science consists of estimating such configurations in particular real settings. We focus on three main issues in this article. First, we discuss the nature of political differences and from this construct an interpretation of the dimensionality of the political space needed to describe a given real setting, underscoring the essentially metaphorical and instrumental use of this concept. Second, we contrast ex ante and ex post interpretations of this dimensionality. Third, we illustrate potential hazards arising from the purely inductive estimation of political spaces using a spatial example from the physical world and political competition in the European Parliament as a political example. [ABSTRACT FROM PUBLISHER]