Abstract and Keywords
This chapter focuses on majority rule processes for choice of a single alternative from a set of alternatives we can regard as locations in one-dimensional space (a line), and where the voters who must choose among these alternatives can themselves be viewed as having a most preferred location on this line, with utility for the voter falling off with distance from each voter’s “ideal point.” The chapter also considers alternatives to this proximity model of voting, such as the directional model, which emphasizes change in direction vis-á-vis the location of the status quo, and the mixed model, which combines directional and proximity components. The chapter briefly reviews some of the main theoretical results on majority rule voting, such as the median voter theorem, and on value restriction and other conditions that avoid cycles. It briefly considers some other types of models that can be studied in the context of choice of alternatives on a line, such as threshold models and models that voters are making judgments rather than expressing preferences. The companion chapter to this one considers applications of the spatial model in the context of one-dimensional politics in areas such as legislative voting, party competition, and coalition formation.
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