3
valence models of candidate positioning. Legislators’ abilities to distribute federal projects are clearly
valence issues providing advantages as challengers do not have access to federal outlays. Further, traits
such as the competence of the incumbent relative to the challenger are clear valence characteristics.
The intuition behind the formal valence theories of position-taking deserve more explanation.
Based on Downs only, where no candidate has any valence advantage, two candidates are expected to
locate at the constituency median. However, if one candidate has a valence advantage (e.g., an incumbent
can send home projects to the district that a challenger cannot) and both candidates still take positions at
the median, then the incumbent with the advantage will win as voters will prefer a candidate with a
valence advantage when both candidates take identical positions. Thus, the non-advantaged candidate
will have an incentive to move off the median toward his or her own most preferred policy position.
Here, somewhat counterintuitively, an incumbent with only a slight advantage (e.g., sends home some
project funding, but not that much) will be better off by remaining close or moving closer to the median in
order to attract votes. However, if an incumbent has a huge valence advantage and a challenger is already
off of the median, the expectation is that the advantaged incumbent can deviate substantially off of the
median and toward his or her own personal preferences (but just not as far away from constituents as the
challenger moves away).
FIGURE 1 HERE
In sum, the valence predictions are non-linear and the distance relationship between legislator and
district is also nonmonotonic. When an incumbent has a slight advantage on valence (e.g., project
allocations), then movement toward the median voter is expected. When an incumbent has a large
advantage on valence, then movement away from the median voter is expected (see Figure 1a).
1
Empirical research on position-taking and representation has often contradicted these theoretical results.
Candidates for Congress represent the views of their party rather than the median voter in their districts
(e.g., Ansolabehere, Snyder and Stewart 2001; Erikson and Wright 2004; Frendreis et al. 2003;
1
In a number of instances, though not tested in this paper, there are no equilibria predictions when a legislator has a
substantial valence advantage and is motivated primarily by office-holding. Empirically, though, I think legislators
and candidates are motivated by both office-holding and policy goals.
Convention