The geometry of voting cycles

It is well known that when all voters in an electorate have preferences con sistent with a single underlying dimension, then the electorate's aggregate preferences must be transitive However, analyses of historical elections s uggest that voters frequently view political alternatives (parties and cand idates) arrayed along not one, but two principal dimensions. Building on ea rlier work by Feld and Grofman, we develop a simple geometric method to rep resent necessary and sufficient conditions for transitive majority decision s 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 a nd parties in recent French and British elections.