A Survey of Equilibrium Analysis in Spatial Models of Elections

Elections, as the institution through which citizens choose their political agents, are at the core of representative democracy. It is therefore appropriate that they occupy a central position in the study of democratic politics. The formal analysis of elections traces back to the work of Hotelling (1929), Downs (1957), and Black (1958), who apply mathematical methods to understand the equilibrium outcomes of elections. This work, and the literature stemming from it, has focused mainly on the positional aspects of electoral campaigns, where we conceptualize candidates as adopting positions in a “space” of possible policies prior to an election. We maintain this focus by considering the main results for the canonical model of elections, in which candidates simultaneously adopt policy platforms and the winner is committed to the platform on which he or she ran. These models abstract from much of the structural detail of elections, including party primary elections, campaign finance and advertising, the role of interest groups, etc. Nevertheless, in order to achieve a deep understanding of elections in their full complexity, it seems that we must address the equilibrium effects of position-taking by candidates in elections.