It is well known that when all voters in an electorate have preferences consistent with a single underlying dimension, then the electorate's aggregate preferences must be transitive. However, analyses of historical elections suggest that voters frequently view political alternatives (parties and candidates) arrayed along not one, but two principal dimensions. Building on earlier work by Feld and Grofman, we develop a simple geometric method to represent necessary and sufficient conditions for transitive majority decisions in two-dimensional policy space. This method provides an intuition as to why transitivity in the two-dimensional case is virtually guaranteed, given realistic positioning by parties and candidates. We illustrate and support our conclusions by analyzing data on the spatial distributions of voters and parties in recent French and British elections.
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