Discretionary Power Causes Divergent Politics

Consider electoral competition between two candidates, in which there is a single-dimensional issue space. The simplest way to get the result that, in Nash equilibrium, candidates propose different policies, is to assume that (1) candidates are uncertain about the distribution of voter preferences, and (2) candidates have preferences over policies. This note shows there is another interesting way to get the result of differentiated equilibrium policies. Assume there is a single-dimensional issue space in which candidates must announce a campaign issue, but there is also a discretionary issue, something on which no position will be taken during the campaign, but the victorious candidate will have the power to implement. For example, the campaign issue could be the tax rate, and the discretionary issue, the appointment of federal judges. It is shown that, if candidates differ on the discretionary issue, and voters know that, then the positions they will announce on the campaign issue will diverge. Indeed, an example is given in which, as the distance between candidates on the discretionary issue becomes large, their equilibrium announcements on the campaign issue converge to their respective ideal points.